{"group":{"group":{"id":18242,"name":"Sequences \u0026 Series IV","lockable":false,"created_at":"2021-04-04T00:37:27.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"The fourth group in a sequence. ","is_default":false,"created_by":46909,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":18,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":3630,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe fourth group in a sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 289.5px 10.5px; transform-origin: 289.5px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 266.5px 10.5px; text-align: left; transform-origin: 266.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe fourth group in a sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2021-04-04T13:56:22.000Z"},"current_player":null},"problems":[{"id":46000,"title":"Compute the harmonic numbers","description":"The nth \u003chttps://mathworld.wolfram.com/HarmonicNumber.html harmonic number\u003e is defined as the sum of the reciprocals of the integers from 1 to n: \r\n\r\n\u003c\u003chttps://mathworld.wolfram.com/images/equations/HarmonicNumber/NumberedEquation1.gif\u003e\u003e\r\n\r\nThe first four harmonic numbers are 1, 3/2, 11/6, and 25/12. The harmonic numbers appear in several interesting identities, including this one for \u003chttps://en.wikipedia.org/wiki/Ap%C3%A9ry's_constant Apery's constant\u003e:\r\n\r\n\u003c\u003chttps://mathworld.wolfram.com/images/equations/RiemannZetaFunction/NumberedEquation34.gif\u003e\u003e\r\n\r\nCompute the nth harmonic number.\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 210px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 105px; transform-origin: 407px 105px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 7.8px; transform-origin: 14px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 7.8px; transform-origin: 5.83333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/HarmonicNumber.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eharmonic number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.083px 7.8px; transform-origin: 201.083px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the sum of the reciprocals of the integers from 1 to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Definition of the harmonic numbers: sum(1/k) from k = 1 to k = n\" style=\"width: 69px; height: 45px;\" width=\"69\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.85px 7.8px; transform-origin: 381.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first four harmonic numbers are 1, 3/2, 11/6, and 25/12. The harmonic numbers appear in several interesting identities, including this one for\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Ap%C3%A9ry's_constant\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eApery's constant\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Relation between zeta(3) and the harmonic numbers\" style=\"width: 98.5px; height: 45px;\" width=\"98.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0167px 7.8px; transform-origin: 42.0167px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.8px 7.8px; transform-origin: 63.8px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth harmonic number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function H = HarmonicNumber(n)\r\n H = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\nH_correct = 1;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 2;\r\nH_correct = 3/2;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 3;\r\nH_correct = 11/6;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 4;\r\nH_correct = 25/12;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 5;\r\nH_correct = 137/60;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 10;\r\nH_correct = 7381/2520;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 15;\r\nH_correct = 1195757/360360;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 20;\r\nH_correct = 55835135/15519504;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nn = 29;\r\nH_correct = 9227046511387/2329089562800;\r\nassert(abs(HarmonicNumber(n)-H_correct)/H_correct \u003c 1e-12)\r\n\r\n%%\r\nfiletext = fileread('HarmonicNumber.m');\r\nx = ~isempty(strfind(filetext, 'A002805')) || ~isempty(strfind(filetext, 'A001008')) ||...\r\n ~isempty(strfind(filetext, '360360'));\r\nassert(~x, 'Illegal approach')","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":94,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-29T03:02:15.000Z","updated_at":"2026-04-05T11:11:33.000Z","published_at":"2020-06-29T03:50:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/HarmonicNumber.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eharmonic number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the sum of the reciprocals of the integers from 1 to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Definition of the harmonic numbers: sum(1/k) from k = 1 to k = n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n = \\\\sum_{k = 1}^n\\\\frac{1}{k}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first four harmonic numbers are 1, 3/2, 11/6, and 25/12. The harmonic numbers appear in several interesting identities, including this one for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Ap%C3%A9ry's_constant\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eApery's constant\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Relation between zeta(3) and the harmonic numbers\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\zeta(3) = \\\\frac{1}{2}\\\\sum_{k = 1}^\\\\infty\\\\frac{H_k}{k^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth harmonic number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46034,"title":"Construct the Seidel-Entringer-Arnold triangle","description":"Several problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems \u003chttps://www.mathworks.com/matlabcentral/cody/problems/37 37\u003e, \u003chttps://www.mathworks.com/matlabcentral/cody/problems/1463 1463\u003e, \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44037 44037\u003e, and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44904 44904\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem \u003chttps://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845 1845\u003e extends Pascal's triangle to a pyramid. Cody Problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle 45460\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients. \r\n\r\nThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\r\n\r\n \r\n 1\r\n 0 1\r\n 1 1 0\r\n 0 1 2 2\r\n 5 5 4 2 0\r\n 0 5 10 14 16 16\r\n 61 61 56 46 32 16 0\r\n 0 61 122 178 224 256 272 272 \r\n \r\nThe name \"secant-tangent triangle\" arises because the sides contain the coefficients in the Taylor series for sec(x) and tan(x):\r\n\r\n sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\r\n tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\r\n\r\nConstruct the nth layer of this triangle. \r\n\r\nHint: Use the boustrophedon (or ox-plowing) rule. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 510.567px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 255.283px; transform-origin: 407px 255.283px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.033px 7.8px; transform-origin: 359.033px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/37\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e37\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1463\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; \"\u003e1463\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44037\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44037\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44904\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44904\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 271.55px 7.8px; transform-origin: 271.55px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e1845\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e extends Pascal's triangle to a pyramid. Cody Problem\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e45460\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.383px 7.8px; transform-origin: 191.383px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.033px 7.8px; transform-origin: 382.033px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.25px; transform-origin: 100.1px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.25px; transform-origin: 115.5px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.25px; transform-origin: 127.05px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.25px; transform-origin: 142.45px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 2 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 5 5 4 2 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 8.25px; transform-origin: 169.4px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 5 10 14 16 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 180.95px 8.25px; transform-origin: 180.95px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 61 61 56 46 32 16 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 196.35px 8.25px; transform-origin: 196.35px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 61 122 178 224 256 272 272\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.917px 7.8px; transform-origin: 333.917px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe name \"secant-tangent triangle\" arises because the sides contain the coefficients in the Taylor series for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sec(x)\" style=\"width: 42px; height: 18.5px;\" width=\"42\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"tan(x)\" style=\"width: 41.5px; height: 18.5px;\" width=\"41.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.0333px; text-align: left; transform-origin: 384px 18.0333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\" style=\"width: 226px; height: 36px;\" width=\"226\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.0333px; text-align: left; transform-origin: 384px 18.0333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe8AAABICAYAAADf530vAAAN4ElEQVR4nO2dPY7rOhKFTzA7cD6BN2BgYgcvNjC545c4fJk3MHD+Iq/B8UTeQyezgF6Dt9ATyAcusSX+idTv+QDh4rZlSyIpHlaxWASEEEIIIYQQQgghhBBCCCGEEEIIIYTwswdwfB9iPI7OcQJwnvSORBc7/K4rexymuzUhxBbZAXgC+DHHE42Yi7oc0C53Hir7+XFBd13xuEx3a0KILfIEcEMj4jsAdzSd0X3Km9oIdzRlLwtu/nyj2yt1hQZcQoiROaIRD8sOTWf0Nf7tbIo9mnLeTX0jIsgB/VMZX2gGwEIIMTk/+C3qoiw3fKYorpDFvUQ4ALtOfSNCCHFG4yKURViXb/yeN71C5b4kOA+ugZcQYlJOAF5oOiWJyDic0A4YlBW3HJ5oBmFCCDEJOzRuXGsNym0+Lmc05f6CBk5LgLEhGmwJIWaBXRIjERmXB5pyP019IyIIB1vKiyCEmA1c/iIRGZcTVO5L4YHGSyKEELPhCInIFLDcZc3NnxeUC0EIUYEDukWAaR59SSUoInKbpzOk3OmKFePSlxyHKYPd90AeEiFEUU74uPM4b207mLP57ImmU+rqtO7v3xFxpJb7v9At5Mx2J+pzQTvK/4V2fdzQH7zJLIRCCFEECjGTR/zgI8JcBnZ7//vAZ277ab57QZM1SlZ3PKnlTtH4fn/OtLQaMI0H64zeDpuf/IbmHbg7fyesR7EB+iycXJQUQISgQHyhaS+uZYH3/+/vc2n1ab51GLHlfoPKfS5QvO9oBlO+tdt7NHWm+toA3LWppODeIPea8EOrmkKi+bk0uFFLKir35WE9IVpnLwDUEW5ywzqjHc/Y1g49OzQd/PV9lHp+Bp1ZF+6a2WPYPtgntL0QuVs8bqHcWdZss3T9+86/Jhx97T/1urHYAZe29hQAmpF3zcbwqPz7Y8Kc2lvKFXxBO8jJzXM9lC1kS6PrP1csr/jUgU84UlhruTMTX1d7faHfy3Dt+U7f77iCnHvdWOyAS56SEZh7IXNOqyZ7NI13yWJ3xO9NGpb8PLGwQ3vhY+25HdOQzn+HT7muccvCrg49Rbz3aAbXXZHGQ+9rreVu3ctPfMrPHl39si2PvoPndHkTc68by8H8jtKdVoZLM+YKo07HCGq4Yrl7L5/wcX0xNeQcxZtrdEvVJzuLG9pWxg6/rZTcsrDlOeWaba6VLV2n3EbTdryxfQIDyTgvXbJs1lruTJvrTk3s0X5md0c6LpMLDY7oPXFFOPe6sdjBFtvDVDBHwGqnDWltzlm8OXc2BhwoDJnvmwNWtOYm3nSrlUqHGFoWxI4s1xK4oOmQ5uAOZL3WfF9TxNt21iUtbmDd5f4N/xSdFUA7yI2NzH6h22Wee91YHmjeN9v/TDXgoodhLVOhLXb4uEzmKt5TiCnXji6ZLYl3qIPIsSbd7/L3XRc8vRxjMTfxttZayU5yzeV+RNgitRva2HKNGRwxY5l7r0OuGwNzGvBa7oDriHHd6KsV7wPacx1faEfo9n3nYs4Ljcz27/P3zv95jZgRGRvTmK6PKa5Zmq2Id2xUdKwg0dV+RnOfL/y2fPi+cJ53TGtwTuJtO+hcNyvZUrnHTBnZsk0VH3qa3Pei9HUP+ESp051v2wB/547P1MqYVvhqxZtLBOzLZ5cMWA7vz7/waQBsIEwLSbiMwQ4MDuiObnS/20XOBu12uZDbWHf4DCD6YANesus8V7zt8pGuZBi+wV0spS3vGGI7JHeO3D3/Evi8NnMSbzsdwXgDu0wvxe2qcm9jRTR18M34gxyhTLmuGxTqnu/GK4xtRKxWvEnoReWceNccCAvn5py/R7tiv9/nUAzsixpyo1DkY2DQxdPcs7UIbGBNSJzd54oldQ1m3zE0mCtVvBm0aOvNtgmb9nCoV2Js8bZu81CHdsCnHLosO6be7Pu8NnMS7x/n3K5lerFLj1TubThYSQ34oss8d9ov5bqn93Ue6O5jWKd9n9dm8+JtRcB9afhZl2UcWqhvNxbog/PdOSJqr8+dbBiscX1f1ydAuS+AHbkOOYY2uCFuczZ6urm4/IyJN4Z2YGOLNzukNSThmYt4u+3c7aDt5iFdfcfSGFu8abWmern6XOa1rztHNi/etqN1rRa7ttYlJB5WIPrgtXOCHKy1xR1vUirxC3nLHEpZ3kNHqkPE27ooKdwll+mNLd5rStM4F/G2npi+98S+g0PnxKdmTPGm0ZJjPAxxmQ+57hzZvHgD3XmJ7brAOYo38GnIORu98/6WyhDxtp3uC3mjcN/AhNbBK3BeidE/ByJLsfxCgz8buFVr2iWmT4id+rLznnOugzmUO+EUROrU1FCXee51p4LR630Hl709Auct5Xl/ETu/Rc5oGscd7U7YZQ7ibTuO1ArasngD7ZiBHEpMHQy1chjjsKSR9xymXVLF23ct68WZc3rTOZQ78PFo5LyzQ1zmQ647FbYNDjmW9MwtYjtK5sq+43fg2VzF23YcqW6knCj3OTFUvDnwyc2QFGN5/wTOG2KpMYfBnAWji1gL8Dtw3pAOKaZP6Nq3uYulbCwyh3LnYDO33ee6zIdedypiLe9n4LzFTufEvFh9I7ra4k33ba54W5FIHY3mup+WGm1uscl7crwWIWrPeS9VuGNgvU49521F2VfOSxHvELXLfaiAcjCV2mctVbhj2PycNxttlwVWW7x5fzkvDD0FHI3eE7+f8x1gPu63IeJ9R1u8S0ee1hTvNQs3MB/xBj7vVqzIL7kTrVnuJQQ0J0p8zcINSLxbk/4uY4h3TtQ3k8oc8WnUKS5wWvw5lb70aHMOenbIH/iEqCneT4SF+4JuV9k/Afyv8vGf7CdrmJN425iXPtejnbrqa4d/oH65/xl4lhC1yp3vWUhAfd7HHdKnB4de90/Ur7M/Ip+lj82Id5+7hZ93CahPgEuJNzOzxULLiyNQ23nQ/fuAv9EuMXjDJUe8Oejh+e7Ah2U71I1eS7zvCGftO6N/MPhvlPGa+I7/5j7cmzmJt7scswsKvM+d+xfql/vfgWcJUaPcY71E98A57K9ijZwS1/0b9evsr8jn6aOGeDNZUCjxTOnzOrEiejA/xh+y7tM7mo6XmXVsEgYmP+nKotZ1U3bvXx/sIHxiy72+mRjfNjjbwdzwiZL38cCyg9WAdjravkbBzR0eaMrOHYnbgQ9Fr4QLvYZ4UyS+0L/HMduc7xn+UfkYSm3xtlZczDXYzuygj/Ddi1l+tLVyt3ElMfty+8qPg+yY2KCS1517ndUQb9sn+jSi9HmdcG2gPU6Bz7n29+D8nVbPHu2t5e5oW0OpeYoZ5d6H/a2ul+s78LmF7qSlulp2+J3d6oHul9Cdn3efeR/4PJcaW4LGjuaXnqyl9tyrXV4Zu8b/+j6XGQyP+LTBUCbDpVCy3N2A0NDh81rYwVaonEtedwnUEG+rh762UPq8Xhhyf0Z3A7C7gZ3Q7vxO5u881xeS3xfeH+PG7ut07f13kbKhRtfuOEshNN/e1Yi5CUlfdPsx8HkOpXcVS4klWHpwTi3xZjvIjcFwNyXh4H4tlCz30BKnlLJn+48RqJLXXQK15rw5OA1pROnzFktMINJQmP98DXl95wwHcSUHBFthj6bclt6xDmVsa17lvjwOaOpsDZ6fRcPdzWq+PDcsey2qqIO1WFzPkw9aoqsdUVfE51G5wT+Qv2C5015LI9Xz1SekqrOVw2joGp3hCc18kDpaQdzYATsXHHK/23iQ0kvttkAojsEnAjbIUtTFBibnxpuozjbCEeHlQKkcKvymWDaMs+AKiyMaa8+Kuc8LZDu1sXZPWwsMlOxbOeCLquY8Z62gPtHGpiANRa73DWJVZxvigLIjNLk2hcU3ReMuPexD4p3PHfk59SUE40HPVGhOmV6UPm+V6kwIUQRa231wuU1sWtClL7kZEy59yp3/tIOmmHXPIp8n4oJOX/Cv4FGdCSGKEOqQaCn4Opq1bMgxNuzI72gEPDVA1QqBAqDqEhPFzXXMJbaXFUKIQcRsvWiTZ8iaiMPm07cHk7/ETG3ZpBdaijg9dJn7pjlVZ0KI6jAyNibZi6yJNE5oZ0N0jy+ELXHr8dCa7OmJGeiqzoQQVaFwx1rSFCJZE+kc0JS3K+bf8LtrGam+1CyJa4IWdSjmQ3UmhKjCGe2I2FgrkN+RNTEMbpoTG0OgCP95EOMyJ6ozIURRmPP7ht+bOoSsQHZesiaGc8BHwEPLk76Rv9RMlCPGZU5UZ0KIqhzRduWG1nrLmiiHzcTlizl4QhH+UxPrMieqMyFEdWyiFp+1cAl8LtKwEfy+IMAH6m9iJPykuMwB1ZkQYiS477XPsj5C1kRpYrZ5jN0iU9QjxWUOqM6EECPBxBLfnnOYD12Ug+Ltc5uvYd/2JcN9AVIyC6rOhBCjYDOBifFgvIGCAOcLvVLaIUwIMTvYQWkN93gwmYemIuaLjUvQAEsIMSp7NELR1/kwYC1kdV/f52idd5gdmjnPK/qXgdFl7lsmtkNT5jdIPKaALvOUQE3VmRCiCHY9sev643rjB/wdDTux1I5sq9jNKdyANHbuL4Q9HYxyDi3jE3WgRyoln7/qTAhRBDeb2vf7b1/vIyawRuKdxh7dqVCfaET7jrhdrCQE02Fd5jF1RVRnQohinNBYDzyOSOuQgEbALxnf2zJDy53u9zPkgh2bPfKWfKnOhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQuTzf1JZ8O9yuTagAAAAAElFTkSuQmCC\" alt=\"tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\" style=\"width: 247.5px; height: 36px;\" width=\"247.5\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.85px 7.8px; transform-origin: 117.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConstruct the nth layer of this triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.883px 7.8px; transform-origin: 152.883px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Use the boustrophedon (or ox-plowing) rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = SeidelEntringerArnold(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct = [1 1 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 5;\r\ny_correct = [5 5 4 2 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 8;\r\ny_correct = [0 61 122 178 224 256 272 272];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%% \r\nn = 13;\r\ny_correct = [2702765 2702765 2652244 2551202 2401024 2204480 1965664 1689872 1383424 1053440 707584 353792 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny = SeidelEntringerArnold(n);\r\ns = sum(y); \r\nv = round(var(y));\r\nd = y([4 6 9]) - y([2 5 7]);\r\ns_correct = 50521;\r\nv_correct = 8277369;\r\nd_correct = [2709 1024 816];\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(v,v_correct) \u0026\u0026 isequal(d,d_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-07T19:46:14.000Z","updated_at":"2025-12-15T13:25:13.000Z","published_at":"2020-07-08T01:44:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/37\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e37\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1463\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1463\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44037\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44037\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44904\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44904\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1845\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e extends Pascal's triangle to a pyramid. Cody Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e45460\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1\\n 0 1\\n 1 1 0\\n 0 1 2 2\\n 5 5 4 2 0\\n 0 5 10 14 16 16\\n 61 61 56 46 32 16 0\\n 0 61 122 178 224 256 272 272]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe name \\\"secant-tangent triangle\\\" arises because the sides contain the coefficients in the Taylor series for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sec(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sec(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"tan(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sec(x) = 1 + 1\\\\frac{x^2}{2!}+5\\\\frac{x^4}{4!}+61\\\\frac{x^6}{6!}+\\\\ldots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan(x) = 1x + 2\\\\frac{x^3}{3!}+16\\\\frac{x^5}{5!}+272\\\\frac{x^7}{7!}+\\\\ldots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConstruct the nth layer of this triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Use the boustrophedon (or ox-plowing) rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46600,"title":"Generate a list of composite numbers","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 57px; transform-origin: 407.5px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.475px 7.875px; transform-origin: 384.475px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePrime numbers get a lot of attention in Cody, while composite numbers get relatively little. Right now a search for \"prime\" on Cody yields 153 problems, while a search for \"composite\" yields only 27--and only eight of those deal with composite numbers. Let's work toward restoring the balance. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.217px 7.875px; transform-origin: 382.217px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the composite numbers less than or equal to the input number. Remember that 1 is neither prime nor composite.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = composites(n)\r\n c = [4 6 etc.];\r\nend","test_suite":"%%\r\nn = 10;\r\nc_correct = [4 6 8 9 10];\r\nassert(isequal(composites(n),c_correct))\r\n\r\n%%\r\nn = 31;\r\nc_correct = [4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30];\r\nassert(isequal(composites(n),c_correct))\r\n\r\n%%\r\nn = 500;\r\nc = composites(n);\r\nlen_correct = 404;\r\nc_correct80 = [110 207 303 399 495];\r\nassert(isequal(length(c),len_correct) \u0026\u0026 isequal(c(80:80:end),c_correct80))\r\n\r\n%%\r\nn = 50011;\r\nc = composites(n);\r\nlen_correct = 44877;\r\nc_correct8900 = [10146 20070 29942 39782 49594];\r\nassert(isequal(length(c),len_correct) \u0026\u0026 isequal(c(8900:8900:end),c_correct8900))\r\n\r\n%%\r\nn = 3628800;\r\nc = composites(n);\r\nlen_correct = 3370110;\r\nc_correct670000 = [728682 1450680 2170682 2889408 3607220];\r\nassert(isequal(length(c),len_correct) \u0026\u0026 isequal(c(670000:670000:end),c_correct670000))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":65,"test_suite_updated_at":"2020-09-22T13:39:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-22T05:11:09.000Z","updated_at":"2026-03-05T10:19:35.000Z","published_at":"2020-09-22T05:33:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers get a lot of attention in Cody, while composite numbers get relatively little. Right now a search for \\\"prime\\\" on Cody yields 153 problems, while a search for \\\"composite\\\" yields only 27--and only eight of those deal with composite numbers. Let's work toward restoring the balance. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the composite numbers less than or equal to the input number. Remember that 1 is neither prime nor composite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46615,"title":"Find terms in the Connell sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.742px 7.79167px; transform-origin: 375.742px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Connell sequence starts with the first odd number and continues with the next two even numbers, the next three odd numbers, the next four even numbers, and so on. Therefore, the first ten terms are 1, 2, 4, 5, 7, 9, 10, 12, 14, and 16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 7.79167px; transform-origin: 373.275px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the terms at the specified positions in the Connell sequence. FOR and WHILE loops are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Connell(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nfiletext = fileread('Connell.m');\r\nnoloops = isempty(strfind(filetext, 'for')) \u0026\u0026 isempty(strfind(filetext, 'while'));\r\nassert(noloops, 'No loops allowed')\r\n\r\n%%\r\nn = 1:10;\r\ny_correct = [1 2 4 5 7 9 10 12 14 16];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 35:40;\r\ny_correct = [62 64 65 67 69 71];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 628:633;\r\ny_correct = [1221 1223 1225 1226 1228 1230];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 1620:1625;\r\ny_correct = 3183:2:3193;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 11111:11111:66666;\r\ny_correct = [22073 44233 66408 88590 110777 132967];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 12457910;\r\ny_correct = 24910828;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 12457910121416;\r\ny_correct = 24915815251257;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 15053\r\ny_correct = 59619;\r\nassert(isequal(Connell(Connell(n)),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2020-12-31T19:26:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-25T12:18:07.000Z","updated_at":"2025-12-09T15:00:13.000Z","published_at":"2020-09-25T13:32:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Connell sequence starts with the first odd number and continues with the next two even numbers, the next three odd numbers, the next four even numbers, and so on. Therefore, the first ten terms are 1, 2, 4, 5, 7, 9, 10, 12, 14, and 16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the terms at the specified positions in the Connell sequence. FOR and WHILE loops are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46676,"title":"List the erauqs","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.825px 8.16667px; transform-origin: 33.825px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter I told \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/players/8608872-jessicar\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eJessicaR\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3917px 8.16667px; transform-origin: 21.3917px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e about \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46624\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.558px 8.16667px; transform-origin: 230.558px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involves the emirps, she asked, \"What about the erauqs?\" As I will do with you, she let me deduce what they are.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.742px 8.16667px; transform-origin: 222.742px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the erauqs less than or equal to the input number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = erauqs(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 99;\r\nassert(isempty(erauqs(n)))\r\n \t\r\n%%\r\nn = 1000;\r\ny_correct = [100 144 169 400 441 900 961];\r\nassert(isequal(erauqs(n),y_correct))\r\n \t\r\n%%\r\nn = 10000;\r\ny_correct = [100 144 169 400 441 900 961 1089 9801 10000];\r\nassert(isequal(erauqs(n),y_correct))\r\n \t\r\n%%\r\nn = 100000;\r\ny = erauqs(n);\r\nlen_correct = 29;\r\nyp_correct = [10404 10609 12100 12544 12769 14400 14884 16900 40000 40401 44100 44521 48400 48841 67600 90000 90601 96100 96721];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(11:29),yp_correct))\r\n\t\r\n%%\r\nn = 1000000;\r\ny = erauqs(n);\r\nlen_correct = 32;\r\nyp_correct = [108900 980100 1000000];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(end-2:end),yp_correct))\r\n \t\r\n%%\r\nn = 1e8;\r\ny = erauqs(n);\r\nlen_correct = 100;\r\nyp_correct = [4456321 4498641 4888521 9678321];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y([76 78 83 94]),yp_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T01:35:23.000Z","updated_at":"2026-02-27T09:58:31.000Z","published_at":"2020-10-06T02:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter I told \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/8608872-jessicar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJessicaR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e about \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46624\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involves the emirps, she asked, \\\"What about the erauqs?\\\" As I will do with you, she let me deduce what they are.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the erauqs less than or equal to the input number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49808,"title":"Identify eban numbers","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 51px; transform-origin: 332px 51px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.642px 7.79167px; transform-origin: 195.642px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProgram a function that will say if an input quantity is in this list:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.717px 7.79167px; transform-origin: 121.717px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46,…\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 21px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 296.758px 7.79167px; transform-origin: 296.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hint is that what is missing from any list quantity (in USA) is also missing from this writing (not including big writing on top and a tag), which was difficult to draft without it. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = iseban(n)\r\n tf = contains(n,something);\r\nend","test_suite":"%%\r\nb = [1 0 1 0 1 0 1 0 0 0];\r\nfor k = 0:99\r\n a(k+1) = iseban(k);\r\nend\r\nassert(isequal(a,[0 0 1 0 1 0 1 zeros(1,23) repmat(b,1,4) zeros(1,30)]));\r\n\r\n%%\r\nassert(~iseban(randi(1900)+99))\r\n\r\n%%\r\nassert(iseban(2000))\r\n\r\n%%\r\nassert(iseban(2006))\r\n\r\n%%\r\nassert(~iseban(2020))\r\n\r\n%%\r\nassert(~iseban(2021))\r\n\r\n%%\r\nassert(iseban(2032))\r\n\r\n%%\r\nassert(iseban(4044))\r\n\r\n%%\r\nassert(~iseban(5056))\r\n\r\n%%\r\nassert(iseban(6066))\r\n\r\n%%\r\nassert(~iseban(7079))\r\n\r\n%%\r\nassert(~iseban(50015))\r\n\r\n%%\r\nassert(iseban(50056))\r\n\r\n%%\r\nassert(~iseban(90210))\r\n\r\n%%\r\nassert(~iseban(floor(10^(5+rand()))))\r\n\r\n%%\r\nassert(iseban(2034056))\r\n\r\n%%\r\nassert(~iseban(8675309))\r\n\r\n%%\r\nassert(iseban(44044044))\r\n\r\n%%\r\nassert(iseban(50044000))\r\n\r\n%%\r\nassert(iseban(66066066))\r\n\r\n%%\r\nassert(~iseban(floor(10^(8+rand()))))\r\n\r\n%%\r\nassert(~iseban(123456789))\r\n\r\n%%\r\nassert(iseban(2002032036))\r\n\r\n%%\r\nassert(iseban(2030006064))\r\n\r\n%%\r\nassert(iseban(6054032056))\r\n\r\n%%\r\nassert(~iseban(floor(10^(11+rand()))))\r\n\r\n%%\r\nassert(iseban(2034056032054))\r\n\r\n%%\r\nassert(~iseban(2034065032054))\r\n\r\n%%\r\nassert(iseban(6054036042034))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-14T15:35:34.000Z","updated_at":"2025-12-15T15:08:49.000Z","published_at":"2021-01-14T15:40:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProgram a function that will say if an input quantity is in this list:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46,…\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hint is that what is missing from any list quantity (in USA) is also missing from this writing (not including big writing on top and a tag), which was difficult to draft without it. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51002,"title":"Deduce the pattern behind the sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 917.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 458.958px; transform-origin: 407px 458.958px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.075px 7.91667px; transform-origin: 60.075px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere's a sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.075px 7.91667px; transform-origin: 37.075px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTricky? Not!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.6px 7.91667px; transform-origin: 46.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou'll deduce it\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 7.91667px; transform-origin: 44.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom this plot.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 7.91667px; transform-origin: 49px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the plot gives \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.0917px 7.91667px; transform-origin: 44.0917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou the blues,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.5667px 7.91667px; transform-origin: 64.5667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe test suite should\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0167px 7.91667px; transform-origin: 63.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProvide some clues.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.9167px 7.91667px; transform-origin: 52.9167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFeeling anxious?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.15px 7.91667px; transform-origin: 41.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou'll be fine.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 7.91667px; transform-origin: 52.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe code I wrote\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.3417px 7.91667px; transform-origin: 51.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIs one short line.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 497.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 248.958px; text-align: left; transform-origin: 384px 248.958px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 657px;height: 492px\" 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\" data-image-state=\"image-loaded\" width=\"657\" height=\"492\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = mysterySeq(n)\r\n a = f(n);\r\nend","test_suite":"%%\r\nassert(isequal(mysterySeq(2),2))\r\n\r\n%%\r\nassert(isequal(mysterySeq(4),4))\r\n\r\n%%\r\nassert(isequal(mysterySeq(9),6))\r\n\r\n%%\r\nassert(isequal(mysterySeq(15),8))\r\n\r\n%%\r\nassert(isequal(mysterySeq(36),10))\r\n\r\n%%\r\nassert(isequal(mysterySeq(35),12))\r\n\r\n%%\r\nassert(isequal(mysterySeq(144),14))\r\n\r\n%%\r\nassert(isequal(mysterySeq(256),16))\r\n\r\n%%\r\nassert(isequal(mysterySeq(315),18))\r\n\r\n%%\r\nassert(isequal(mysterySeq(441),20))\r\n\r\n%%\r\nassert(isequal(mysterySeq(495),22))\r\n\r\n%%\r\nassert(isequal(mysterySeq(143),24))\r\n\r\n%%\r\nassert(isequal(mysterySeq(169),26))\r\n\r\n%%\r\nassert(isequal(mysterySeq(115),28))\r\n\r\n%%\r\nassert(isequal(mysterySeq(4802),30))\r\n\r\n%%\r\nassert(isequal(mysterySeq(65536),32))\r\n\r\n%%\r\nassert(isequal(mysterySeq(62500),34))\r\n\r\n%%\r\nassert(isequal(mysterySeq(186),36))\r\n\r\n%%\r\nassert(isequal(mysterySeq(361),38))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1048576),40))\r\n\r\n%%\r\nassert(isequal(mysterySeq(117649),42))\r\n\r\n%%\r\nassert(isequal(mysterySeq(14641),44))\r\n\r\n%%\r\nassert(isequal(mysterySeq(529),46))\r\n\r\n%%\r\nassert(isequal(mysterySeq(116875),48))\r\n\r\n%%\r\nassert(isequal(mysterySeq(301),50))\r\n\r\n%%\r\nassert(isequal(mysterySeq(235),52))\r\n\r\n%%\r\nassert(isequal(mysterySeq(329),54))\r\n\r\n%%\r\nassert(isequal(mysterySeq(159),56))\r\n\r\n%%\r\nassert(isequal(mysterySeq(517),58))\r\n\r\n%%\r\nassert(isequal(mysterySeq(3486784401),60))\r\n\r\n%%\r\nassert(isequal(mysterySeq(444125),62))\r\n\r\n%%\r\nassert(isequal(mysterySeq(96049800),64))\r\n\r\n%%\r\nassert(isequal(mysterySeq(31381059609),66))\r\n\r\n%%\r\nassert(isequal(mysterySeq(533715),68))\r\n\r\n%%\r\nassert(isequal(mysterySeq(282475249),70))\r\n\r\n%%\r\nassert(isequal(mysterySeq(36501),72))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1369),74))\r\n\r\n%%\r\nassert(isequal(mysterySeq(130321),76))\r\n\r\n%%\r\nassert(isequal(mysterySeq(46023),78))\r\n\r\n%%\r\nassert(isequal(mysterySeq(576650390625),80))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1172889),82))\r\n\r\n%%\r\nassert(isequal(mysterySeq(13841287201),84))\r\n\r\n%%\r\nassert(isequal(mysterySeq(22755),86))\r\n\r\n%%\r\nassert(isequal(mysterySeq(2133),88))\r\n\r\n%%\r\nassert(isequal(mysterySeq(8033333),90))\r\n\r\n%%\r\nassert(isequal(mysterySeq(267),92))\r\n\r\n%%\r\nassert(isequal(mysterySeq(102656268),94))\r\n\r\n%%\r\nassert(isequal(mysterySeq(16168),96))\r\n\r\n%%\r\nassert(isequal(mysterySeq(228125),98))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1125899906842624),100))\r\n\r\n%%\r\np = primes(1e4); k = randi(length(p));\r\nassert(isequal(mysterySeq(p(k)),p(k)))\r\n\r\n%%\r\nassert(isequal(mysterySeq(mysterySeq(mysterySeq(mysterySeq(mysterySeq(mysterySeq(50014)))))),5))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2021-03-18T00:35:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-17T02:24:34.000Z","updated_at":"2025-12-15T15:32:30.000Z","published_at":"2021-03-17T02:29:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere's a sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTricky? Not!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou'll deduce it\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom this plot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the plot gives \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou the blues,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite should\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProvide some clues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFeeling anxious?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou'll be fine.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe code I wrote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIs one short line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"492\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"657\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49572,"title":"Compute the largest number possible with the Brussels choice","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 235.633px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117.817px; transform-origin: 407px 117.817px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.208px 7.79167px; transform-origin: 374.208px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Brussels choice (or Choix de Bruxelles) operation changes one number to another by taking a substring of the digits and either doubling it or (if the number is even) halving it. For example, starting with 9 and highlighting substrings, one can generate this sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e18\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.79167px; transform-origin: 7.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, 3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.6667px 7.79167px; transform-origin: 11.6667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e22\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 7.79167px; transform-origin: 11.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e644\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.79167px; transform-origin: 7.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 7.79167px; transform-origin: 35px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e88, 1488,...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7417px 7.79167px; transform-origin: 65.7417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAnother possibility is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.79167px; transform-origin: 7.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.2917px 7.79167px; transform-origin: 11.2917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e116\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 7.79167px; transform-origin: 11.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e232\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e46\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.79167px; transform-origin: 7.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e92\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 18\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e44\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2167px 7.79167px; transform-origin: 27.2167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, 1888,...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 296.767px 7.79167px; transform-origin: 296.767px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBoth of these excerpts have eight entries, but the second ends in a larger number than the first. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.6333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.8167px; text-align: left; transform-origin: 384px 21.8167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.008px 7.79167px; transform-origin: 129.008px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an initial value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABPElEQVRYhe2WTRGDMBBGnwccxAAGUFAFdYADHNRCNCABD1hAAxbaQ3aHNCRp2kJ7yZvJgSzsx/4FoFKpVCqVP9ECPTAAnex1ct2eKToBi4h3gAVm4C7LnCF8FecL0AS2u2f7qbAvfjta+OI57yJ288L+MQ2wiuMxcY9mZSWeFcO+OYsY2KJKdfEk9inx/CqiBteYqSB2aNQxx4hTfbkhsGm5em9PS/SyN3KOlYl0ZhbiozfjgsqOpJ/yS8Tes2UmrHfr7YdY9hl5S/yKi2zkuSxWntMmnDN+bU5c316dN7IGtnnXyK0sbSYVyInHbE9oZP4a2VK8BvslAsXi4FI+4GoUNknqY3KY+CfomOXEi+f9XXSeYx+aom7/ltyc507MQ8idcNkxO4ob29ne4KLWsf0JBtdkp/5iVSqVIh6VmIITWgIeSQAAAABJRU5ErkJggg==\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.417px 7.79167px; transform-origin: 112.417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the largest number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABNklEQVRYhe2WW7GDMBBAjwccYAADUYCCOMABDq4FNCAhHmqhGrDA/WB3ss2E0mGS9idnJh9kyS77DNBoNBqNxo8YgAmYASd7Tp6HmkYD8BTjDliAB7DL6msY9qL8CXSJbDeyrxq2xv9KGx6NcpeR9xfy23TAJorXk3c0Khv5qNxmJnp1VsVB5KGkYYhenyl25uPmkoY/URy4jswtbMjHjHwiRqZqvlPjnqPtVl7TsvAapUHOennuRe65YDDGA4dnnRzWflfPF1m2I/S9nSNKXvRssi4noXpm10oM8Zbsp+jYnYgDSOvkozE8ihdT5sC7y6QjTkXbLbt8VFV0+FgvtYOKj+GUhVgPihZxrnuKosVmU6X5ropeNja3WgOB+B9QBc237XnNd6DCPWDRDkmn3iSr0Wj8hn/n1nOR3s62vwAAAABJRU5ErkJggg==\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.2833px 7.79167px; transform-origin: 46.2833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting after \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63px 7.79167px; transform-origin: 63px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e steps. In the above examples, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABPElEQVRYhe2WTRGDMBBGnwccxAAGUFAFdYADHNRCNCABD1hAAxbaQ3aHNCRp2kJ7yZvJgSzsx/4FoFKpVCqVP9ECPTAAnex1ct2eKToBi4h3gAVm4C7LnCF8FecL0AS2u2f7qbAvfjta+OI57yJ288L+MQ2wiuMxcY9mZSWeFcO+OYsY2KJKdfEk9inx/CqiBteYqSB2aNQxx4hTfbkhsGm5em9PS/SyN3KOlYl0ZhbiozfjgsqOpJ/yS8Tes2UmrHfr7YdY9hl5S/yKi2zkuSxWntMmnDN+bU5c316dN7IGtnnXyK0sbSYVyInHbE9oZP4a2VK8BvslAsXi4FI+4GoUNknqY3KY+CfomOXEi+f9XXSeYx+aom7/ltyc507MQ8idcNkxO4ob29ne4KLWsf0JBtdkp/5iVSqVIh6VmIITWgIeSQAAAABJRU5ErkJggg==\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.425px 7.79167px; transform-origin: 27.425px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 9 and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.517px 7.79167px; transform-origin: 129.517px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Return the number as a character string.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = ChoixdeBruxelles(a0,n)\r\n% a0 = initial value in the sequence\r\n% n = number of steps\r\n a = f(n);\r\nend","test_suite":"%%\r\na0 = 1;\r\nn = 0;\r\na_correct = '1';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 1;\r\nn = 4;\r\na_correct = '16';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 1;\r\nn = 5;\r\na_correct = '112';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 1;\r\nn = 10;\r\na_correct = '88224';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 1;\r\nn = 20;\r\na_correct = '811281128164416';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 1;\r\nn = 30;\r\na_correct = '8112811281128112811288224';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 1;\r\nn = 50;\r\na_correct = '811281128112811281128112811281128112811288224';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 2;\r\nn = 29;\r\na_correct = '8112811281128112811288224';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 3;\r\nn = 20;\r\na_correct = '11281128112816448';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 7;\r\nn = 4;\r\na_correct = '2112';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 7;\r\nn = 15;\r\na_correct = '1681128164416';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 7;\r\nn = 50;\r\na_correct = '168112811281128112811281128112811281128112816448';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 29;\r\nn = 6;\r\na_correct = '844416';\r\nassert(isequal(ChoixdeBruxelles(a0,n),a_correct))\r\n\r\n%%\r\na0 = 11;\r\nn = 37;\r\na_correct = '412316860416';\r\nassert(isequal(num2str(prod(ChoixdeBruxelles(a0,n)-'0')),a_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2021-01-02T23:31:04.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-12-23T22:47:46.000Z","updated_at":"2025-12-16T15:11:43.000Z","published_at":"2020-12-23T23:16:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Brussels choice (or Choix de Bruxelles) operation changes one number to another by taking a substring of the digits and either doubling it or (if the number is even) halving it. For example, starting with 9 and highlighting substrings, one can generate this sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e18\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e2, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e22\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e644\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e88, 1488,...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother possibility is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e116\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e232\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e46\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e4, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e92\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e4, 18\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, 1888,...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBoth of these excerpts have eight entries, but the second ends in a larger number than the first. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an initial value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the largest number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting after \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e steps. In the above examples, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 9 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Return the number as a character string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49803,"title":"Compute expulsions from the Kimberling shuffle","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 155.583px; transform-origin: 407px 155.583px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.983px 7.79167px; transform-origin: 368.983px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.8917px 7.79167px; transform-origin: 10.8917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.05px 7.79167px; transform-origin: 26.05px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.79167px; transform-origin: 20.6167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eexcept\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 235.725px 7.79167px; transform-origin: 235.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 2 3 4 5 6 7 8 9 10...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e2 3 4 5 6 7 8 9 10 11...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e4 2 5 6 7 8 9 10 11 12...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e6 2 7 4 8 9 10 11 12 13...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 157.85px 8.25px; transform-origin: 157.85px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 146.3px 8.25px; transform-origin: 146.3px 8.25px; \"\u003e8 7 9 2 10 6 11 12 13 14.\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.25px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.25px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.008px 7.79167px; transform-origin: 369.008px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the row after which the input number is expelled. For example, because 5 appears on the main diagonal of row 3, your function should return 3. An optional challenge is to determine whether all numbers are eventually expelled from the array.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = KimberlingExpulsion(m)\r\n n = f(m);\r\nend","test_suite":"%%\r\nm = 1;\r\nn_correct = 1;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 5;\r\nn_correct = 3;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 10;\r\nn_correct = 5;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 18;\r\nn_correct = 11;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 19;\r\nn_correct = 49595;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 23;\r\nn_correct = 24;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 27;\r\nn_correct = 7598;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 31;\r\nn_correct = 13;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n%%\r\nm = 37;\r\nn_correct = 58;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 40;\r\nn_correct = 93167;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 43;\r\nn_correct = 1523;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 46;\r\nn_correct = 20;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 50;\r\nn_correct = 123;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 89;\r\nn_correct = 15803;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 101;\r\nn_correct = 95;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 108;\r\nn_correct = 63;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 117;\r\nn_correct = 390;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 8899;\r\nn_correct = 76973;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 8979;\r\nn_correct = 3465;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 1691;\r\nn_correct = 32633;\r\nassert(isequal(KimberlingExpulsion(KimberlingExpulsion(KimberlingExpulsion(m))),n_correct));\r\n\r\n%%\r\nk = randi(14);\r\nm = 9*2^k-3*k-10;\r\nn_correct = 3*(2^k-1);\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nfiletext = fileread('KimberlingExpulsion.m');\r\ncheating = contains(filetext, 'urlread') || contains(filetext, 'oeis'); \r\nassert(~cheating)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-09T19:48:53.000Z","updated_at":"2025-12-16T21:01:56.000Z","published_at":"2021-01-09T19:57:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexcept\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 2 3 4 5 6 7 8 9 10...\\n2 3 4 5 6 7 8 9 10 11...\\n4 2 5 6 7 8 9 10 11 12...\\n6 2 7 4 8 9 10 11 12 13...\\n8 7 9 2 10 6 11 12 13 14....]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the row after which the input number is expelled. For example, because 5 appears on the main diagonal of row 3, your function should return 3. An optional challenge is to determine whether all numbers are eventually expelled from the array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51282,"title":"Compute a row of the Kimberling shuffle","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 320.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.083px; transform-origin: 407px 160.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.2417px 7.91667px; transform-origin: 90.2417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem continues from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/18242/problems/49803\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 49803\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.983px 7.91667px; transform-origin: 368.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.8917px 7.91667px; transform-origin: 10.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.05px 7.91667px; transform-origin: 26.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eexcept\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 235.725px 7.91667px; transform-origin: 235.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 2 3 4 5 6 7 8 9 10...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e2 3 4 5 6 7 8 9 10 11...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e4 2 5 6 7 8 9 10 11 12...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e6 2 7 4 8 9 10 11 12 13...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 157.85px 7.91667px; transform-origin: 157.85px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; \"\u003e8 7 9 2 10 6 11 12 13 14.\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 7.91667px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.4333px 7.91667px; transform-origin: 99.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 277.208px 7.91667px; transform-origin: 277.208px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth row of this array, up to and including the first number beyond which the numbers are in order. For example, given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.7417px 7.91667px; transform-origin: 86.7417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e your function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[8 7 9 2 10 6 11]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = KimberlingShuffleRow(n)\r\n r = 1:n;\r\nend","test_suite":"%%\r\nn = 1;\r\nr_correct = 1;\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 2;\r\nr_correct = 2;\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 3;\r\nr_correct = [4 2 5];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 5;\r\nr_correct = [8 7 9 2 10 6 11];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 26;\r\nr_correct = [60 58 44 48 26 54 65 64 16 30 19 45 51 50 66 34 38 29 47 40 32 49 67 63 39 55 56 12 41 61 68 13 59 25 69 57 37 17 70 62 27 52 71 43 72 11 73 21 74];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 53;\r\nr_correct = [101 118 73 81 43 56 68 21 88 131 136 71 143 32 45 110 40 142 119 109 57 72 77 80 19 90 61 51 144 114 49 112 134 93 124 92 69 102 121 111 39 16 74 85 145 129 27 47 17 141 108 94 67 127 132 64 50 98 38 29 146 96 137 139 117 128 130 41 147 107 100 37 120 75 30 106 148 113 103 12 63 140 89 104 149 123 126 87 150 66 105 78 151 135 86 125 152 116 153 60 154 133 155];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 151;\r\nr_correct = [383 377 319 392 360 103 85 187 375 136 299 309 125 432 398 258 270 410 40 411 189 372 168 311 380 74 231 176 306 167 123 425 239 159 284 295 393 17 335 206 205 260 282 386 133 363 171 337 433 152 139 387 196 242 340 57 127 424 254 417 142 226 381 388 288 357 150 241 199 323 217 56 43 287 385 308 368 431 365 155 215 60 32 170 268 420 419 312 303 253 105 63 251 220 356 314 89 324 145 404 193 106 116 371 137 184 203 225 274 333 237 182 434 291 427 113 262 132 301 202 294 397 317 98 423 409 224 339 329 272 180 281 345 164 163 66 102 78 154 428 252 207 195 197 435 300 396 292 289 367 112 322 334 148 77 332 415 179 384 266 304 320 257 181 213 351 173 390 256 348 261 364 394 235 418 354 436 313 117 305 209 107 407 328 290 190 273 338 280 265 344 92 219 111 395 325 271 248 68 330 353 370 183 27 277 430 326 336 437 416 185 421 315 399 379 422 400 234 94 177 391 346 426 267 438 298 69 316 307 369 279 297 412 143 285 247 250 186 401 342 439 246 343 310 188 134 362 19 149 293 131 276 278 201 405 406 440 361 373 359 212 218 296 118 441 378 321 429 331 350 318 109 442 214 87 140 259 403 347 129 443 414 413 147 444 269 174 349 445 51 408 286 446 221 447 240 448 75 449];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nr1 = KimberlingShuffleRow(1776);\r\nr2 = KimberlingShuffleRow(r1(1));\r\nsum_correct = 9180392;\r\nassert(isequal(sum(r2),sum_correct))\r\n\r\n%%\r\nr1 = KimberlingShuffleRow(4881);\r\nr2 = KimberlingShuffleRow(r1(1));\r\nsump_correct = 11284849;\r\nassert(isequal(sum(r2(isprime(r2))),sump_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-04T13:38:50.000Z","updated_at":"2025-12-16T21:10:34.000Z","published_at":"2021-04-04T13:48:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem continues from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/18242/problems/49803\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 49803\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexcept\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 2 3 4 5 6 7 8 9 10...\\n2 3 4 5 6 7 8 9 10 11...\\n4 2 5 6 7 8 9 10 11 12...\\n6 2 7 4 8 9 10 11 12 13...\\n8 7 9 2 10 6 11 12 13 14....]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth row of this array, up to and including the first number beyond which the numbers are in order. For example, given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e your function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[8 7 9 2 10 6 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50953,"title":"Round up to π","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.35px 7.91667px; transform-origin: 191.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo commemorate Pi Day (March 14 in the U.S.), compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.85px 7.91667px; transform-origin: 117.85px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in a sequence by starting with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 7.91667px; transform-origin: 62.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounding up to the next multiple of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAkCAYAAAA0EkzVAAABX0lEQVRoge2X0Y2DMBBEXw90kAaugVRABXRAB3SQFq6GlJAe0gI10AL3Ya+8BEeCWwuwtE/aj8iKzU4mOwYcx3EcxzmHBujPfogr0QADMMVyCA6ZgDmWC0MQ5U5wzIgLk+WFC5PFhflCUWF+gDaW0AAdYcq3uS9dFLMwvdpEqotrLcsJP1OPOMUc81YbiUtGwpRvScI8rAcdRDFhJN6eBDFGgkDEzyLM3XrQQRQR5kZqvCc5RRhYumnrnoOxutWu2ykiTEcSZmT9fvEkuWkr2mX/rT3nfVJEGGl8jht+ot20lRKOsQz6IsJI8kyEyNboX/5mOeRgzMLoxn8z6w/SX6wmzMJI4zNrt0CKcYnpWlxjFkYazzlCp5W8tb7IC3g1TMI0pMaHzHrPcr68sUXokegL6250TOcubnp9byqdhaShfu6B7fcvIIgh0fiNPq7XMFt0P6Xj33Ecx3Ecx6mJP74PqN5v6wByAAAAAElFTkSuQmCC\" alt=\"n-1\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.242px 7.91667px; transform-origin: 111.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounding up to the next multiple of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n-2\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.908px 7.91667px; transform-origin: 171.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and so on to rounding up to the next multiple of 1. For example, with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.467px 7.91667px; transform-origin: 244.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence—\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(n)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.6417px 7.91667px; transform-origin: 19.6417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 22. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.325px 7.91667px; transform-origin: 96.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(n)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 7.91667px; transform-origin: 15.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.517px 7.91667px; transform-origin: 122.517px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. Also compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n^2/f(n)\" style=\"width: 52.5px; height: 20px;\" width=\"52.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.8417px 7.91667px; transform-origin: 68.8417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and notice its limit as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1083px 7.91667px; transform-origin: 17.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gets large. For more on this limit, see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathpages.com/home/kmath001/kmath001.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethis page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2167px 7.91667px; transform-origin: 48.2167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by K.S. Brown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a,y] = roundUpToPi(n)\r\n a = f(n);\r\n y = n^2/a;\r\nend","test_suite":"%%\r\nn = 1;\r\na_correct = 1;\r\ny_correct = 1;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 2;\r\na_correct = 2;\r\ny_correct = 2;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 8;\r\na_correct = 22;\r\ny_correct = 2.909090909090909;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31;\r\na_correct = 322;\r\ny_correct = 2.984472049689441;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 314;\r\na_correct = 31422;\r\ny_correct = 3.137801540322067;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 3141;\r\na_correct = 3143652;\r\ny_correct = 3.138350237240;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31415;\r\na_correct = 314162898;\r\ny_correct = 3.141371025295291;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 314159;\r\na_correct = 31416153708;\r\ny_correct = 3.141564629404888;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 3141592;\r\na_correct = 3141592912272;\r\ny_correct = 3.141591087728265;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31415926;\r\na_correct = 314159277765514;\r\ny_correct = 3.141592422344870;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9) \r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-15T04:19:17.000Z","updated_at":"2026-03-16T11:10:09.000Z","published_at":"2021-03-15T04:33:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo commemorate Pi Day (March 14 in the U.S.), compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in a sequence by starting with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounding up to the next multiple of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n-1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounding up to the next multiple of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n-2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and so on to rounding up to the next multiple of 1. For example, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence—\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 22. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. Also compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n^2/f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^2/f(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and notice its limit as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gets large. For more on this limit, see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathpages.com/home/kmath001/kmath001.htm\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by K.S. Brown.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46122,"title":"Find the nth term in the digit inventory sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 308.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 154.433px; transform-origin: 407px 154.433px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/2/problems/40\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e40\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/2/problems/55\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e55\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/27/problems/594\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e594\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276.5px 8px; transform-origin: 276.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deal with the \"look and say\" sequence, in which each term describes the term before it. For example, the first few terms of sequence \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A001151\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eA001151\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168px 8px; transform-origin: 168px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the Online Encyclopedia of Integer Sequences are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 164px 8.5px; transform-origin: 164px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 8, 18, 1118, 3118, 132118, 1113122118\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375px 8px; transform-origin: 375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe second term is \"one 8\". The third is \"one 1, one 8\". The fourth is \"three 1's, one 1\". Et cetera. That is, each term is constructed by naming the runs of digits in the previous term. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the sequence that I will call the \"digit inventory sequence\", each term is constructed as an inventory of the digits. If the first term is 8, then the first six terms are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 156px 8.5px; transform-origin: 156px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 8, 18, 1118, 3118, 211318, 31121318\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first four terms match those in the look-and-say, but the next terms differ. For example, because the fourth term has two 1's, one 3, and one 8, the fifth term is 211318. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the first term of a digit inventory sequence and finds the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term. Output the term as a character string.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = digitInventory(n,y1)\r\n y(1) = y1;\r\n y(n) = ...;\r\nend","test_suite":"%%\r\nn = 1;\r\ny1 = 8;\r\ny_correct = '8';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 6;\r\ny1 = 8;\r\ny_correct = '31121318';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 11;\r\ny1 = 8;\r\ny_correct = '3122331418';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 12;\r\ny1 = 8;\r\ny_correct = '3122331418';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 13;\r\ny1 = 1;\r\ny_correct = '21322314';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny1 = 1;\r\ny_correct = '21322314';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 8;\r\ny1 = 46122;\r\ny_correct = '3122331416';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 5;\r\ny1 = 1234567890;\r\ny_correct = '101112213141516171819';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny1 = 1234567890;\r\ny_correct = '101112213141516171819';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 9;\r\ny1 = 134567890;\r\ny_correct = '10714213141516172819';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny1 = 134567890;\r\ny_correct = '10812213241516271819';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny1 = 134567890;\r\ny_correct = '10714213141516172819';\r\nassert(isequal(digitInventory(n,y1),y_correct))\r\n\r\n%%\r\nn = 54;\r\ny1 = 134567890;\r\ny_correct = '10812213241516271819';\r\nassert(isequal(digitInventory(n,y1),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-08-12T03:51:19.000Z","updated_at":"2025-12-16T21:16:11.000Z","published_at":"2020-08-12T04:40:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/2/problems/40\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e40\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/2/problems/55\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/27/problems/594\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e594\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deal with the \\\"look and say\\\" sequence, in which each term describes the term before it. For example, the first few terms of sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A001151\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eA001151\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in the Online Encyclopedia of Integer Sequences are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 8, 18, 1118, 3118, 132118, 1113122118]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe second term is \\\"one 8\\\". The third is \\\"one 1, one 8\\\". The fourth is \\\"three 1's, one 1\\\". Et cetera. That is, each term is constructed by naming the runs of digits in the previous term. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the sequence that I will call the \\\"digit inventory sequence\\\", each term is constructed as an inventory of the digits. If the first term is 8, then the first six terms are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 8, 18, 1118, 3118, 211318, 31121318]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first four terms match those in the look-and-say, but the next terms differ. For example, because the fourth term has two 1's, one 3, and one 8, the fifth term is 211318. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the first term of a digit inventory sequence and finds the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term. Output the term as a character string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46571,"title":"Characterize the final state of the digit inventory sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 317.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 158.65px; transform-origin: 407px 158.65px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46122-find-the-nth-term-in-the-digit-inventory-sequence\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46122\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.533px 7.91667px; transform-origin: 313.533px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a counting sequence that I called the digit inventory sequence, in which each term provides an inventory of the digits of the previous term. If the initial number of the sequence is 24, then the sequence is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 304.15px 7.91667px; transform-origin: 304.15px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 265.65px 7.91667px; transform-origin: 265.65px 7.91667px; \"\u003e 24, 1214, 211214, 312214, 21221314, 31321314, 31123314, 31123314, \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 7.91667px; \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 26.95px 7.91667px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 26.95px 7.91667px; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.91667px; transform-origin: 384px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the third term provides an inventory of the second: two 1's, one 2, one 4. Notice that starting with 24 leads to a steady state after 7 terms because all subsequent terms are equal to the seventh (i.e., 31123314). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.133px 7.91667px; transform-origin: 136.133px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, the final state is not necessarily a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003esteady\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.125px 7.91667px; transform-origin: 178.125px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e state. If the starting number is 210, then the sequence is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 331.1px 7.91667px; transform-origin: 331.1px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 210, 101112, 104112, 10311214, 1041121314, 1051121324, 104122131415, 105122132415, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 292.6px 7.91667px; transform-origin: 292.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 281.05px 7.91667px; transform-origin: 281.05px 7.91667px; \"\u003e 104132131425, 104122232415, 103142132415, 104122232415, 103142132415, \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 7.91667px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.91667px; transform-origin: 384px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe tenth and eleventh terms repeat indefinitely. In other words, the repeated terms start at term 10, and they have a period of 2. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.875px 7.91667px; transform-origin: 372.875px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the number of the term at which the final state begins and the period of the repeated terms.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [n,period] = digInvFinalState(y1)\r\n n = f1(y1);\r\n period = f2(y1);\r\nend","test_suite":"%%\r\ny1 = 24;\r\nn_correct = 7;\r\nperiod_correct = 1;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = 210;\r\nn_correct = 10;\r\nperiod_correct = 2;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = 1;\r\nn_correct = 13;\r\nperiod_correct = 1;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = 10;\r\nn_correct = 10;\r\nperiod_correct = 1;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = 22;\r\nn_correct = 1;\r\nperiod_correct = 1;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = 40;\r\nn_correct = 10;\r\nperiod_correct = 2;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = 50;\r\nn_correct = 11;\r\nperiod_correct = 3;\r\n[n,period] = digInvFinalState(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\nfor y1 = 567:571\r\n [n(y1-566),period(y1-566)] = digInvFinalState(y1);\r\nend\r\nprod_correct = 136;\r\nassert(isequal(n*period',prod_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-08-29T02:58:19.000Z","updated_at":"2025-12-16T21:25:08.000Z","published_at":"2020-08-29T04:10:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46122-find-the-nth-term-in-the-digit-inventory-sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46122\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a counting sequence that I called the digit inventory sequence, in which each term provides an inventory of the digits of the previous term. If the initial number of the sequence is 24, then the sequence is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 24, 1214, 211214, 312214, 21221314, 31321314, 31123314, 31123314, ... ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the third term provides an inventory of the second: two 1's, one 2, one 4. Notice that starting with 24 leads to a steady state after 7 terms because all subsequent terms are equal to the seventh (i.e., 31123314). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, the final state is not necessarily a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esteady\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e state. If the starting number is 210, then the sequence is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 210, 101112, 104112, 10311214, 1041121314, 1051121324, 104122131415, 105122132415, \\n 104132131425, 104122232415, 103142132415, 104122232415, 103142132415, ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe tenth and eleventh terms repeat indefinitely. In other words, the repeated terms start at term 10, and they have a period of 2. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the number of the term at which the final state begins and the period of the repeated terms.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51246,"title":"Characterize the final state of another digit inventory sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 370.433px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 185.217px; transform-origin: 407px 185.217px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 7.91667px; transform-origin: 49.7917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46122-find-the-nth-term-in-the-digit-inventory-sequence\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e46122\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46571\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e46571\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.525px 7.91667px; transform-origin: 264.525px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a digit inventory sequence in which one term in the sequence describes the previous. For example, if one term is 411, the next would be 2114: two 1’s, one 4. For some starting numbers, the sequence reaches a steady state, but for others, the terms oscillate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.283px 7.91667px; transform-origin: 210.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA different form of a digit inventory is formed by listing the counts of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.00833px 7.91667px; transform-origin: 7.00833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eall\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 158.325px 7.91667px; transform-origin: 158.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits—in the order 1-9 and 0—and concatenating them for the next term in the sequence. If the initial seed is 570, then the next three terms would be \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 130.9px 7.91667px; transform-origin: 130.9px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e0000101001, 3000000007, 0010001008\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361.7px 7.91667px; transform-origin: 361.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first term arises because 570 has zero 1s, 2s, 3s, and 4s; one 5; zero 6s, one 7; zero 8s and 9s; and one 0. The second term arises because the first has three 1s, seven 0s, and zero of everything else. If we continue to generate terms, we will find that the seventh and eighth terms will repeat. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.933px 7.91667px; transform-origin: 381.933px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAt first, I thought that this sequence always reaches a state in which these same two terms oscillate, but I have since found a few seeds that lead to a steady state. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.817px 7.91667px; transform-origin: 381.817px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a seed as a string and determines the number of the term at which the final state begins and the period of the repeated terms. Take the initial seed to be term 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.042px 7.91667px; transform-origin: 371.042px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: The function is not required to return the terms themselves, but the terms in the final state are interesting. The seeds in the test suite lead to only two sets of final terms. Can you find seeds that lead to different final terms? \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [n,period] = digitInventory2(y1)\r\n n = f1(y1);\r\n period = f2(y1);\r\nend","test_suite":"%%\r\ny1 = '1';\r\nn_correct = 7;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '53';\r\nn_correct = 7;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '100';\r\nn_correct = 6;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '570';\r\nn_correct = 7;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '1000';\r\nn_correct = 6;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '1002';\r\nn_correct = 5;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '10023';\r\nn_correct = 4;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '10234';\r\nn_correct = 8;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '11111';\r\nn_correct = 7;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '12345';\r\nn_correct = 8;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '11233344';\r\nn_correct = 4;\r\nperiod_correct = 1;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '112233344';\r\nn_correct = 4;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '11223334444';\r\nn_correct = 4;\r\nperiod_correct = 1;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '112233344445';\r\nn_correct = 6;\r\nperiod_correct = 1;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '1111111111';\r\nn_correct = 8;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '1234567890';\r\nn_correct = 9;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))\r\n\r\n%%\r\ny1 = '122333444455555666666777777788888888999999999';\r\nn_correct = 10;\r\nperiod_correct = 2;\r\n[n,period] = digitInventory2(y1);\r\nassert(isequal(n,n_correct) \u0026\u0026 isequal(period,period_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-27T22:51:08.000Z","updated_at":"2025-12-16T21:32:44.000Z","published_at":"2021-03-27T23:42:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46122-find-the-nth-term-in-the-digit-inventory-sequence\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e46122\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46571\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e46571\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e involved a digit inventory sequence in which one term in the sequence describes the previous. For example, if one term is 411, the next would be 2114: two 1’s, one 4. For some starting numbers, the sequence reaches a steady state, but for others, the terms oscillate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA different form of a digit inventory is formed by listing the counts of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eall\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits—in the order 1-9 and 0—and concatenating them for the next term in the sequence. If the initial seed is 570, then the next three terms would be \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[0000101001, 3000000007, 0010001008]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first term arises because 570 has zero 1s, 2s, 3s, and 4s; one 5; zero 6s, one 7; zero 8s and 9s; and one 0. The second term arises because the first has three 1s, seven 0s, and zero of everything else. If we continue to generate terms, we will find that the seventh and eighth terms will repeat. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAt first, I thought that this sequence always reaches a state in which these same two terms oscillate, but I have since found a few seeds that lead to a steady state. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a seed as a string and determines the number of the term at which the final state begins and the period of the repeated terms. Take the initial seed to be term 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOptional: The function is not required to return the terms themselves, but the terms in the final state are interesting. The seeds in the test suite lead to only two sets of final terms. Can you find seeds that lead to different final terms? \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50811,"title":"Compute the nth term from the Sieve of Flavius Josephus","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo apply the Sieve of Eratosthenes, start with the natural numbers (skipping 1), keep the first number (i.e., 2), and delete all multiples (4, 6, 8, 10, etc.). Then repeat: keep the first remaining number (3) and delete all multiples (9, 15, 21, etc.). The remaining numbers are the primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.5px 8px; transform-origin: 247.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo apply the Sieve of Flavius Josephus, start with the natural numbers. On the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth step, remove every \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(k+1)\" style=\"width: 46px; height: 18.5px;\" width=\"46\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.5px 8px; transform-origin: 23.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003est term remaining after the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(k-1)\" style=\"width: 46px; height: 18.5px;\" width=\"46\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 296px 8px; transform-origin: 296px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003est step. So, on the first step, remove every second number (2, 4, 6, 8, etc.) to leave 1, 3, 5, 7, 9, 11, 13, 15, 17…On the second step, remove every third number (5, 11, 17, etc.) to leave 1, 3, 7, 9, 13, 15, 19,… \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100.5px 8px; transform-origin: 100.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 254px 8px; transform-origin: 254px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in the sequence remaining after the Sieve of Flavius Josephus is applied.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FlaviusJosephus(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct = 7;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 7;\r\ny_correct = 39;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 2187;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 923;\r\ny_correct = 669121;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 1967;\r\ny_correct = 3039399;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 3449;\r\ny_correct = 9340303;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 6141;\r\ny_correct = 29614789;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 9460;\r\ny_correct = 70290691;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 23403;\r\ny_correct = 430160191;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n\r\n%%\r\nn = 27182818;\r\ny_correct = 580335113880043;\r\nassert(isequal(FlaviusJosephus(n),y_correct))\r\n \r\n%%\r\nn = 67;\r\ny_correct = 9781407;\r\nassert(isequal(FlaviusJosephus(FlaviusJosephus(n)),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-03-09T03:38:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-09T02:19:47.000Z","updated_at":"2025-12-17T13:21:36.000Z","published_at":"2021-03-09T02:40:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo apply the Sieve of Eratosthenes, start with the natural numbers (skipping 1), keep the first number (i.e., 2), and delete all multiples (4, 6, 8, 10, etc.). Then repeat: keep the first remaining number (3) and delete all multiples (9, 15, 21, etc.). The remaining numbers are the primes. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo apply the Sieve of Flavius Josephus, start with the natural numbers. On the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth step, remove every \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(k+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(k+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003est term remaining after the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(k-1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(k-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003est step. So, on the first step, remove every second number (2, 4, 6, 8, etc.) to leave 1, 3, 5, 7, 9, 11, 13, 15, 17…On the second step, remove every third number (5, 11, 17, etc.) to leave 1, 3, 7, 9, 13, 15, 19,… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in the sequence remaining after the Sieve of Flavius Josephus is applied.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50913,"title":"Compute the nth term from the golden sieve","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.5px 8px; transform-origin: 129.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved the Sieve of Eratosthenes, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811-compute-the-nth-term-from-the-sieve-of-flavius-josephus\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved the Sieve of Flavius Josephus. To apply the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003egolden sieve\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.5px 8px; transform-origin: 133.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, start with the natural numbers and at the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth step, take the sequence, which we will call \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n)\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 8px; transform-origin: 30.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 119.5px 8px; transform-origin: 119.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the first step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position to get 2, 3, 4, 5, 6, 7,…Then in the second step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(2) = 3\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256px 8px; transform-origin: 256px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position (i.e., 4) to get 2, 3, 5, 6, 7, 8, 9,…In the third step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(3) = 5\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7167px 8px; transform-origin: 52.7167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position (i.e., 7) to get 2, 3, 5, 6, 8, 9, 10,…Et cetera.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.5px 8px; transform-origin: 178.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in the sequence after an infinite number of steps.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = goldenSieve(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 6; \r\ny_correct = 10;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16; \r\ny_correct = 26;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 60; \r\ny_correct = 97;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 616; \r\ny_correct = 997;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1666; \r\ny_correct = 2696;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6066; \r\ny_correct = 9815;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16166; \r\ny_correct = 26157;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 66616; \r\ny_correct = 107787;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 166666; \r\ny_correct = 269671;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 606606; \r\ny_correct = 981509;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 161161616; \r\ny_correct = 260764972;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6161161616; \r\ny_correct = 9968968905;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 616161161616; \r\ny_correct = 996969702042;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-12T02:43:21.000Z","updated_at":"2025-12-17T13:39:40.000Z","published_at":"2021-03-12T02:52:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved the Sieve of Eratosthenes, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811-compute-the-nth-term-from-the-sieve-of-flavius-josephus\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved the Sieve of Flavius Josephus. To apply the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egolden sieve\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, start with the natural numbers and at the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth step, take the sequence, which we will call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the first step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position to get 2, 3, 4, 5, 6, 7,…Then in the second step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(2) = 3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(2) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position (i.e., 4) to get 2, 3, 5, 6, 7, 8, 9,…In the third step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(3) = 5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(3) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position (i.e., 7) to get 2, 3, 5, 6, 8, 9, 10,…Et cetera.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in the sequence after an infinite number of steps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}