{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":55715,"title":"AZPC Oddly Triangular: N=35/305 using Digits 3/7/9  Part 5 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nPart 5 is a generalization of multiple solutions to find Rokicki's result.\r\nReviewing the N=8/11/14 3/7/9 solutions determine a form such that N=5+3*n.\r\nThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri5p3n_379(N) where N=digit length, M is a string of length 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: 255px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.5px; transform-origin: 407px 127.5px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 214.5px 8px; transform-origin: 214.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePart 5 is a generalization of multiple solutions to find Rokicki's result.\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: 243.5px 8px; transform-origin: 243.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReviewing the N=8/11/14 3/7/9 solutions determine a form such that N=5+3*n.\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: 304.5px 8px; transform-origin: 304.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 223.5px 8px; transform-origin: 223.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri5p3n_379(N) where N=digit length, M is a string of length N.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri5p3n_379(N)\r\n% M needs to be a string of length N\r\n M='339';\r\n  \r\nend","test_suite":"%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 35;\r\n\r\nM=OddlyTri5p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nelse\r\n fprintf('Not Valid: \\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 305;\r\n\r\nM=OddlyTri5p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nelse\r\n fprintf('Not Valid: \\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:38:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-14T03:11:12.000Z","updated_at":"2022-09-14T03:38:07.000Z","published_at":"2022-09-14T03:38:07.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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\u003ePart 5 is a generalization of multiple solutions to find Rokicki's result.\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\u003eReviewing the N=8/11/14 3/7/9 solutions determine a form such that N=5+3*n.\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 values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri5p3n_379(N) where N=digit length, M is a string of length N.\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":55710,"title":"AZPC Oddly Triangular: N=34/304 using Digits 3/7/9  Part 4 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nPart 4 is the generalization of multiple solutions to find Rokicki's result.\r\nReviewing the N=7/10/13 3/7/9 solutions determine a form such that N=4+3*n.\r\nThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri4p3n_379(N) where N=digit length, M is a string of length 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: 255px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.5px; transform-origin: 407px 127.5px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 220.5px 8px; transform-origin: 220.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePart 4 is the generalization of multiple solutions to find Rokicki's result.\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: 244px 8px; transform-origin: 244px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReviewing the N=7/10/13 3/7/9 solutions determine a form such that N=4+3*n.\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: 304.5px 8px; transform-origin: 304.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 223.5px 8px; transform-origin: 223.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri4p3n_379(N) where N=digit length, M is a string of length N.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri4p3n_379(N)\r\n% M needs to be a string of length N\r\n M='339';\r\n  \r\nend","test_suite":"%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 34;\r\n\r\nM=OddlyTri4p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nelse\r\n fprintf('Not Valid: \\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 304;\r\n\r\nM=OddlyTri4p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nelse\r\n fprintf('Not Valid: \\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:36:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-14T02:51:43.000Z","updated_at":"2022-09-14T03:36:05.000Z","published_at":"2022-09-14T03:36:05.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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\u003ePart 4 is the generalization of multiple solutions to find Rokicki's result.\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\u003eReviewing the N=7/10/13 3/7/9 solutions determine a form such that N=4+3*n.\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 values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri4p3n_379(N) where N=digit length, M is a string of length N.\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":55705,"title":"AZPC Oddly Triangular: N=10/11/13/14 Digits 3/7/9  Part 3 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nThis is step three of the steps and processing types to find Rokicki's result.\r\nThis challenge is to find a solution subset with lengths 10, 11, 13, and 14 that only use the digits 3/7/9 in M and begin with 339 (10/11), 3399(13), and 33999(14). The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for N\u003e8 solutions as the eps is \u003e1 for the sums.\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri339_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.","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: 246px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 123px; transform-origin: 407px 123px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 235.5px 8px; transform-origin: 235.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is step three of the steps and processing types to find Rokicki's result.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to find a solution subset with lengths 10, 11, 13, and 14 that only use the digits 3/7/9 in M and begin with 339 (10/11), 3399(13), and 33999(14). The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for N\u0026gt;8 solutions as the eps is \u0026gt;1 for the sums.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 342px 8px; transform-origin: 342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri339_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri339_379(N,Q)\r\n% M starts with 339\r\n M=zeros(Q,1);\r\n  \r\nend\r\n\r\nfunction cc = zcombvec(old, new)\r\n% old: base matrix\r\n% new: column vector of new elements to augment combinations\r\n% cc: matrix of all combinations of old with new\r\n%{ \r\n Usage \r\n a=[3];\r\n b=[3;7;9];\r\n for ih=2:2\r\n  a=zcombvec(a,b);\r\n end\r\n results in [3 3;3 7; 3 9]\r\n%}\r\n mm = size(old,1);\r\n nn = size(new,1);\r\n cc = repmat(old, nn, 1);\r\n t=repmat(new', mm, 1);\r\n cc = [cc  t(:)];\r\nend %zcombvec\r\n\r\nfunction Nsum=sum1NJava(N)\r\n% 1+2+...+N= N*(N+1)/2  Nsum=sum(1:N)\r\n% N may be either string or real\r\n% No commas allowed in N if it is a string\r\n% Nsum char\r\n import java.math.*\r\n \r\n BD1=BigDecimal(1); % Create a BigDecimal Constant\r\n BD2=BigDecimal(2);\r\n \r\n numval=BigDecimal(N); % N\r\n numval1=numval.add(BD1); % N+1\r\n numval1d2=numval1.divide(BD2);\r\n m1m2=numval.multiply(numval1d2);\r\n Nsum=char(m1m2);\r\nend %sum1NJava","test_suite":"%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 10;\r\nQ = 1;\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums using java math infinite precision\r\n  numval=BigDecimal(M); % M\r\n  numval1=numval.add(BD1); % M+1\r\n  numval1d2=numval1.divide(BD2); %(M+1)/2\r\n  m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n  Msum=char(m1m2); %Convert Java variable to a string\r\n  if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n  if nnz(Msum=='2')\u003e0,valid=0;end\r\n  if nnz(Msum=='4')\u003e0,valid=0;end\r\n  if nnz(Msum=='6')\u003e0,valid=0;end\r\n  if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 11;\r\nQ = 2;\r\nMsumc{Q}='';\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=1;\r\n for i=1:Q\r\n  valid=valid*prod(mod(prod(num2str(M(i))-'0',2),2));\r\n  if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M(i)); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n   Msumc{i}=Msum;\r\n  end\r\n end % for i 1:Q\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 13;\r\nQ = 3;\r\nMsumc{Q}='';\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=1;\r\n for i=1:Q\r\n  valid=valid*prod(mod(prod(num2str(M(i))-'0',2),2));\r\n  if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M(i)); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n   Msumc{i}=Msum;\r\n  end\r\n end % for i 1:Q\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 14;\r\nQ = 1;\r\nMsumc{Q}='';\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=1;\r\n for i=1:Q\r\n  valid=valid*prod(mod(prod(num2str(M(i))-'0',2),2));\r\n  if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M(i)); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n   Msumc{i}=Msum;\r\n  end\r\n end % for i 1:Q\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:33:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T23:14:10.000Z","updated_at":"2022-09-14T03:33:28.000Z","published_at":"2022-09-14T03:33:28.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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 is step three of the steps and processing types to find Rokicki's result.\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 challenge is to find a solution subset with lengths 10, 11, 13, and 14 that only use the digits 3/7/9 in M and begin with 339 (10/11), 3399(13), and 33999(14). The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for N\u0026gt;8 solutions as the eps is \u0026gt;1 for the sums.\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri339_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\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":55695,"title":"AZPC Oddly Triangular: N=8/9 Digits 3/7/9  Part 2 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nThis is step two of the steps and processing types to find Rokicki's result.\r\nThis challenge is to find a solution subset with lengths 8 and 9 that only use the digits 3/7/9 in M. The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for the N=9 solution as the eps is 8 for the sum. There are 8 length 8 solutions if all odd digits are allowed. Rokicki focused on patterns using only 3/7/9 to reduce his search space.\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.","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: 246px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 123px; transform-origin: 407px 123px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 229.5px 8px; transform-origin: 229.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is step two of the steps and processing types to find Rokicki's result.\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: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to find a solution subset with lengths 8 and 9 that only use the digits 3/7/9 in M. The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for the N=9 solution as the eps is 8 for the sum. There are 8 length 8 solutions if all odd digits are allowed. Rokicki focused on patterns using only 3/7/9 to reduce his search space.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 330px 8px; transform-origin: 330px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri_379(N,Q)\r\n M=zeros(Q,1);\r\n  \r\nend\r\n\r\nfunction cc = zcombvec(old, new)\r\n% old: base matrix\r\n% new: column vector of new elements to augment combinations\r\n% cc: matrix of all combinations of old with new\r\n%{ \r\n Usage \r\n a=[3];\r\n b=[3;7;9];\r\n for ih=2:2\r\n  a=zcombvec(a,b);\r\n end\r\n results in [3 3;3 7; 3 9]\r\n%}\r\n mm = size(old,1);\r\n nn = size(new,1);\r\n cc = repmat(old, nn, 1);\r\n t=repmat(new', mm, 1);\r\n cc = [cc  t(:)];\r\nend %zcombvec\r\n\r\nfunction Nsum=sum1NJava(N)\r\n% 1+2+...+N= N*(N+1)/2  Nsum=sum(1:N)\r\n% N may be either string or real\r\n% No commas allowed in N if it is a string\r\n% Nsum char\r\n import java.math.*\r\n \r\n BD1=BigDecimal(1); % Create a BigDecimal Constant\r\n BD2=BigDecimal(2);\r\n \r\n numval=BigDecimal(N); % N\r\n numval1=numval.add(BD1); % N+1\r\n numval1d2=numval1.divide(BD2);\r\n m1m2=numval.multiply(numval1d2);\r\n Nsum=char(m1m2);\r\nend %sum1NJava","test_suite":"%%\r\ntic\r\nN = 8;\r\nQ = 2;\r\nvalid = 0;\r\nM=OddlyTri_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 9;\r\nQ = 1;\r\nvalid = 0;\r\nM=OddlyTri_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums using java math infinite precision\r\n  numval=BigDecimal(M); % M\r\n  numval1=numval.add(BD1); % M+1\r\n  numval1d2=numval1.divide(BD2); %(M+1)/2\r\n  m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n  Msum=char(m1m2); %Convert Java variable to a string\r\n  if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n  if nnz(Msum=='2')\u003e0,valid=0;end\r\n  if nnz(Msum=='4')\u003e0,valid=0;end\r\n  if nnz(Msum=='6')\u003e0,valid=0;end\r\n  if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:27:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T17:29:39.000Z","updated_at":"2022-09-14T03:27:56.000Z","published_at":"2022-09-14T03:27:56.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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 is step two of the steps and processing types to find Rokicki's result.\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 challenge is to find a solution subset with lengths 8 and 9 that only use the digits 3/7/9 in M. The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for the N=9 solution as the eps is 8 for the sum. There are 8 length 8 solutions if all odd digits are allowed. Rokicki focused on patterns using only 3/7/9 to reduce his search space.\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\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":55680,"title":"AZPC Oddly Triangular: Small N  Part 1 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nThis challenge sequence shall step thru the steps and processing types to find Rokicki's result.\r\nThis challenge is to find all solutions with lengths 1 thru 7.\r\nM=OddlyTri_1(N,Q) where N=digit length, Q=number of solutions, M is a vector of the Q values.\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: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 298.5px 8px; transform-origin: 298.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge sequence shall step thru the steps and processing types to find Rokicki's result.\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: 181px 8px; transform-origin: 181px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to find all solutions with lengths 1 thru 7.\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: 298.5px 8px; transform-origin: 298.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri_1(N,Q) where N=digit length, Q=number of solutions, M is a vector of the Q values.\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 8px; transform-origin: 0px 8px; 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 M=OddlyTri_1(N,Q)\r\n  M=zeros(Q,1);\r\nend","test_suite":"%%\r\ntic\r\nN = 1;\r\nQ = 2;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 2;\r\nQ = 2;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 3;\r\nQ = 1;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 4;\r\nQ = 4;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 5;\r\nQ = 4;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 6;\r\nQ = 6;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 7;\r\nQ = 3;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:22:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T16:00:45.000Z","updated_at":"2022-09-14T03:22:22.000Z","published_at":"2022-09-14T03:22:22.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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 challenge sequence shall step thru the steps and processing types to find Rokicki's result.\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 challenge is to find all solutions with lengths 1 thru 7.\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\u003eM=OddlyTri_1(N,Q) where N=digit length, Q=number of solutions, M is a vector of the Q values.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":55715,"title":"AZPC Oddly Triangular: N=35/305 using Digits 3/7/9  Part 5 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nPart 5 is a generalization of multiple solutions to find Rokicki's result.\r\nReviewing the N=8/11/14 3/7/9 solutions determine a form such that N=5+3*n.\r\nThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri5p3n_379(N) where N=digit length, M is a string of length 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: 255px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.5px; transform-origin: 407px 127.5px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 214.5px 8px; transform-origin: 214.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePart 5 is a generalization of multiple solutions to find Rokicki's result.\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: 243.5px 8px; transform-origin: 243.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReviewing the N=8/11/14 3/7/9 solutions determine a form such that N=5+3*n.\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: 304.5px 8px; transform-origin: 304.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 223.5px 8px; transform-origin: 223.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri5p3n_379(N) where N=digit length, M is a string of length N.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri5p3n_379(N)\r\n% M needs to be a string of length N\r\n M='339';\r\n  \r\nend","test_suite":"%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 35;\r\n\r\nM=OddlyTri5p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nelse\r\n fprintf('Not Valid: \\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 305;\r\n\r\nM=OddlyTri5p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nelse\r\n fprintf('Not Valid: \\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:38:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-14T03:11:12.000Z","updated_at":"2022-09-14T03:38:07.000Z","published_at":"2022-09-14T03:38:07.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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\u003ePart 5 is a generalization of multiple solutions to find Rokicki's result.\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\u003eReviewing the N=8/11/14 3/7/9 solutions determine a form such that N=5+3*n.\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 values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri5p3n_379(N) where N=digit length, M is a string of length N.\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":55710,"title":"AZPC Oddly Triangular: N=34/304 using Digits 3/7/9  Part 4 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nPart 4 is the generalization of multiple solutions to find Rokicki's result.\r\nReviewing the N=7/10/13 3/7/9 solutions determine a form such that N=4+3*n.\r\nThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri4p3n_379(N) where N=digit length, M is a string of length 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: 255px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.5px; transform-origin: 407px 127.5px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 220.5px 8px; transform-origin: 220.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePart 4 is the generalization of multiple solutions to find Rokicki's result.\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: 244px 8px; transform-origin: 244px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReviewing the N=7/10/13 3/7/9 solutions determine a form such that N=4+3*n.\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: 304.5px 8px; transform-origin: 304.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 223.5px 8px; transform-origin: 223.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri4p3n_379(N) where N=digit length, M is a string of length N.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri4p3n_379(N)\r\n% M needs to be a string of length N\r\n M='339';\r\n  \r\nend","test_suite":"%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 34;\r\n\r\nM=OddlyTri4p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nelse\r\n fprintf('Not Valid: \\n')\r\n fprintf('%s %s\\n',M,Msum)\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 304;\r\n\r\nM=OddlyTri4p3n_379(N) % M is a string\r\nvalid=length(M)==N;\r\n if nnz(M=='0')\u003e0,valid=0;end % Check for any Even digits in M\r\n if nnz(M=='2')\u003e0,valid=0;end\r\n if nnz(M=='4')\u003e0,valid=0;end\r\n if nnz(M=='6')\u003e0,valid=0;end\r\n if nnz(M=='8')\u003e0,valid=0;end\r\n   \r\n if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\n\r\n\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nelse\r\n fprintf('Not Valid: \\n')\r\n for i=1:50:length(M)\r\n  fprintf('%s\\n',M(i:min(length(M),i+49)))\r\n end\r\n fprintf('\\n')\r\n for i=1:50:length(Msum)\r\n  fprintf('%s\\n',Msum(i:min(length(Msum),i+49)))\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:36:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-14T02:51:43.000Z","updated_at":"2022-09-14T03:36:05.000Z","published_at":"2022-09-14T03:36:05.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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\u003ePart 4 is the generalization of multiple solutions to find Rokicki's result.\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\u003eReviewing the N=7/10/13 3/7/9 solutions determine a form such that N=4+3*n.\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 values 397979797973 and 399799799799799733 has N=6+6*n given the generalization of  3[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]9[n]7[1]3[n]\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri4p3n_379(N) where N=digit length, M is a string of length N.\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":55705,"title":"AZPC Oddly Triangular: N=10/11/13/14 Digits 3/7/9  Part 3 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nThis is step three of the steps and processing types to find Rokicki's result.\r\nThis challenge is to find a solution subset with lengths 10, 11, 13, and 14 that only use the digits 3/7/9 in M and begin with 339 (10/11), 3399(13), and 33999(14). The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for N\u003e8 solutions as the eps is \u003e1 for the sums.\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri339_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.","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: 246px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 123px; transform-origin: 407px 123px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 235.5px 8px; transform-origin: 235.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is step three of the steps and processing types to find Rokicki's result.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to find a solution subset with lengths 10, 11, 13, and 14 that only use the digits 3/7/9 in M and begin with 339 (10/11), 3399(13), and 33999(14). The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for N\u0026gt;8 solutions as the eps is \u0026gt;1 for the sums.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 342px 8px; transform-origin: 342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri339_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri339_379(N,Q)\r\n% M starts with 339\r\n M=zeros(Q,1);\r\n  \r\nend\r\n\r\nfunction cc = zcombvec(old, new)\r\n% old: base matrix\r\n% new: column vector of new elements to augment combinations\r\n% cc: matrix of all combinations of old with new\r\n%{ \r\n Usage \r\n a=[3];\r\n b=[3;7;9];\r\n for ih=2:2\r\n  a=zcombvec(a,b);\r\n end\r\n results in [3 3;3 7; 3 9]\r\n%}\r\n mm = size(old,1);\r\n nn = size(new,1);\r\n cc = repmat(old, nn, 1);\r\n t=repmat(new', mm, 1);\r\n cc = [cc  t(:)];\r\nend %zcombvec\r\n\r\nfunction Nsum=sum1NJava(N)\r\n% 1+2+...+N= N*(N+1)/2  Nsum=sum(1:N)\r\n% N may be either string or real\r\n% No commas allowed in N if it is a string\r\n% Nsum char\r\n import java.math.*\r\n \r\n BD1=BigDecimal(1); % Create a BigDecimal Constant\r\n BD2=BigDecimal(2);\r\n \r\n numval=BigDecimal(N); % N\r\n numval1=numval.add(BD1); % N+1\r\n numval1d2=numval1.divide(BD2);\r\n m1m2=numval.multiply(numval1d2);\r\n Nsum=char(m1m2);\r\nend %sum1NJava","test_suite":"%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 10;\r\nQ = 1;\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums using java math infinite precision\r\n  numval=BigDecimal(M); % M\r\n  numval1=numval.add(BD1); % M+1\r\n  numval1d2=numval1.divide(BD2); %(M+1)/2\r\n  m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n  Msum=char(m1m2); %Convert Java variable to a string\r\n  if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n  if nnz(Msum=='2')\u003e0,valid=0;end\r\n  if nnz(Msum=='4')\u003e0,valid=0;end\r\n  if nnz(Msum=='6')\u003e0,valid=0;end\r\n  if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 11;\r\nQ = 2;\r\nMsumc{Q}='';\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=1;\r\n for i=1:Q\r\n  valid=valid*prod(mod(prod(num2str(M(i))-'0',2),2));\r\n  if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M(i)); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n   Msumc{i}=Msum;\r\n  end\r\n end % for i 1:Q\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 13;\r\nQ = 3;\r\nMsumc{Q}='';\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=1;\r\n for i=1:Q\r\n  valid=valid*prod(mod(prod(num2str(M(i))-'0',2),2));\r\n  if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M(i)); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n   Msumc{i}=Msum;\r\n  end\r\n end % for i 1:Q\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 14;\r\nQ = 1;\r\nMsumc{Q}='';\r\nvalid = 0;\r\nM=OddlyTri339_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=1;\r\n for i=1:Q\r\n  valid=valid*prod(mod(prod(num2str(M(i))-'0',2),2));\r\n  if valid % Now calc sums using java math infinite precision\r\n   numval=BigDecimal(M(i)); % M\r\n   numval1=numval.add(BD1); % M+1\r\n   numval1d2=numval1.divide(BD2); %(M+1)/2\r\n   m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n   Msum=char(m1m2); %Convert Java variable to a string\r\n   if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n   if nnz(Msum=='2')\u003e0,valid=0;end\r\n   if nnz(Msum=='4')\u003e0,valid=0;end\r\n   if nnz(Msum=='6')\u003e0,valid=0;end\r\n   if nnz(Msum=='8')\u003e0,valid=0;end\r\n   Msumc{i}=Msum;\r\n  end\r\n end % for i 1:Q\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msumc{i})\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:33:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T23:14:10.000Z","updated_at":"2022-09-14T03:33:28.000Z","published_at":"2022-09-14T03:33:28.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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 is step three of the steps and processing types to find Rokicki's result.\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 challenge is to find a solution subset with lengths 10, 11, 13, and 14 that only use the digits 3/7/9 in M and begin with 339 (10/11), 3399(13), and 33999(14). The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for N\u0026gt;8 solutions as the eps is \u0026gt;1 for the sums.\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri339_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\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":55695,"title":"AZPC Oddly Triangular: N=8/9 Digits 3/7/9  Part 2 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nThis is step two of the steps and processing types to find Rokicki's result.\r\nThis challenge is to find a solution subset with lengths 8 and 9 that only use the digits 3/7/9 in M. The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for the N=9 solution as the eps is 8 for the sum. There are 8 length 8 solutions if all odd digits are allowed. Rokicki focused on patterns using only 3/7/9 to reduce his search space.\r\nUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\r\nM=OddlyTri_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.","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: 246px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 123px; transform-origin: 407px 123px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 229.5px 8px; transform-origin: 229.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is step two of the steps and processing types to find Rokicki's result.\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: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to find a solution subset with lengths 8 and 9 that only use the digits 3/7/9 in M. The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for the N=9 solution as the eps is 8 for the sum. There are 8 length 8 solutions if all odd digits are allowed. Rokicki focused on patterns using only 3/7/9 to reduce his search space.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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: 330px 8px; transform-origin: 330px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M=OddlyTri_379(N,Q)\r\n M=zeros(Q,1);\r\n  \r\nend\r\n\r\nfunction cc = zcombvec(old, new)\r\n% old: base matrix\r\n% new: column vector of new elements to augment combinations\r\n% cc: matrix of all combinations of old with new\r\n%{ \r\n Usage \r\n a=[3];\r\n b=[3;7;9];\r\n for ih=2:2\r\n  a=zcombvec(a,b);\r\n end\r\n results in [3 3;3 7; 3 9]\r\n%}\r\n mm = size(old,1);\r\n nn = size(new,1);\r\n cc = repmat(old, nn, 1);\r\n t=repmat(new', mm, 1);\r\n cc = [cc  t(:)];\r\nend %zcombvec\r\n\r\nfunction Nsum=sum1NJava(N)\r\n% 1+2+...+N= N*(N+1)/2  Nsum=sum(1:N)\r\n% N may be either string or real\r\n% No commas allowed in N if it is a string\r\n% Nsum char\r\n import java.math.*\r\n \r\n BD1=BigDecimal(1); % Create a BigDecimal Constant\r\n BD2=BigDecimal(2);\r\n \r\n numval=BigDecimal(N); % N\r\n numval1=numval.add(BD1); % N+1\r\n numval1d2=numval1.divide(BD2);\r\n m1m2=numval.multiply(numval1d2);\r\n Nsum=char(m1m2);\r\nend %sum1NJava","test_suite":"%%\r\ntic\r\nN = 8;\r\nQ = 2;\r\nvalid = 0;\r\nM=OddlyTri_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\nimport java.math.*\r\nBD1=BigDecimal(1); % Create a BigDecimal Constant\r\nBD2=BigDecimal(2);\r\ntic\r\nN = 9;\r\nQ = 1;\r\nvalid = 0;\r\nM=OddlyTri_379(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums using java math infinite precision\r\n  numval=BigDecimal(M); % M\r\n  numval1=numval.add(BD1); % M+1\r\n  numval1d2=numval1.divide(BD2); %(M+1)/2\r\n  m1m2=numval.multiply(numval1d2); %M*(M+1)/2\r\n  Msum=char(m1m2); %Convert Java variable to a string\r\n  if nnz(Msum=='0')\u003e0,valid=0;end % Check for any Even digits in sum\r\n  if nnz(Msum=='2')\u003e0,valid=0;end\r\n  if nnz(Msum=='4')\u003e0,valid=0;end\r\n  if nnz(Msum=='6')\u003e0,valid=0;end\r\n  if nnz(Msum=='8')\u003e0,valid=0;end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  %fprintf('%i\\n',M(i))\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %s\\n',M(i),Msum)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:27:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T17:29:39.000Z","updated_at":"2022-09-14T03:27:56.000Z","published_at":"2022-09-14T03:27:56.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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 is step two of the steps and processing types to find Rokicki's result.\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 challenge is to find a solution subset with lengths 8 and 9 that only use the digits 3/7/9 in M. The sum(1:M(i)) may only use odd digits. Normal double variables will not suffice for the N=9 solution as the eps is 8 for the sum. There are 8 length 8 solutions if all odd digits are allowed. Rokicki focused on patterns using only 3/7/9 to reduce his search space.\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\u003eUsage of matlab java math can be seen in the Test Suite. A function zcombvec is given in the function template to facilitate creation of all vectors that only use the 3/7/9 digits. Usage of zcombvec is not required.\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\u003eM=OddlyTri_379(N,Q) where N=digit length, Q=number of solutions, M is a double vector of the Q values.\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":55680,"title":"AZPC Oddly Triangular: Small N  Part 1 of 5","description":"AZPC created the Oddly Triangular contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\r\nThis challenge sequence shall step thru the steps and processing types to find Rokicki's result.\r\nThis challenge is to find all solutions with lengths 1 thru 7.\r\nM=OddlyTri_1(N,Q) where N=digit length, Q=number of solutions, M is a vector of the Q values.\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: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; 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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAZPC\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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e created the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOddly Triangular\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: 270.5px 8px; transform-origin: 270.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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: 298.5px 8px; transform-origin: 298.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge sequence shall step thru the steps and processing types to find Rokicki's result.\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: 181px 8px; transform-origin: 181px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to find all solutions with lengths 1 thru 7.\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: 298.5px 8px; transform-origin: 298.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eM=OddlyTri_1(N,Q) where N=digit length, Q=number of solutions, M is a vector of the Q values.\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 8px; transform-origin: 0px 8px; 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 M=OddlyTri_1(N,Q)\r\n  M=zeros(Q,1);\r\nend","test_suite":"%%\r\ntic\r\nN = 1;\r\nQ = 2;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 2;\r\nQ = 2;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 3;\r\nQ = 1;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 4;\r\nQ = 4;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 5;\r\nQ = 4;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 6;\r\nQ = 6;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc\r\n%%\r\ntic\r\nN = 7;\r\nQ = 3;\r\nvalid = 0;\r\nM=OddlyTri_1(N,Q)\r\nM(M\u003c10^(N-1))=[]; %Verify digit lengths\r\nM(M\u003e=10^N)=[];\r\nM=unique(M);\r\nif length(M)==Q\r\n valid=prod(mod(prod(num2str(M)-'0',2),2));\r\n if valid % Now calc sums\r\n  Msum=M.*(M+1)/2;\r\n  for i=1:length(M)\r\n   valid=valid*prod(mod(prod(num2str(Msum(i))-'0',2),2));\r\n  end\r\n end\r\nend % length(M)==Q\r\nif valid\r\n fprintf('Valid set\\n')\r\n for i=1:length(M)\r\n  fprintf('%i\\n',M(i))\r\n end\r\nelse\r\n fprintf('Not Valid set: Q %i required\\n',Q)\r\n for i=1:length(M)\r\n  fprintf('%i %i\\n',M(i),M(i)*(M(i)+1)/2)\r\n end\r\nend\r\n\r\nassert(isequal(valid,1))\r\ntoc","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2022-09-14T03:22:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T16:00:45.000Z","updated_at":"2022-09-14T03:22:22.000Z","published_at":"2022-09-14T03:22:22.000Z","restored_at":null,"restored_by":null,"spam":null,"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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAZPC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e created the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOddly Triangular\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contest on 9/7/22. The challenge is to find the longest sequence of N odd digits such that sum(1:value)  is composed of only odd digits. The contest ended on 9/8/22 as Rokicki created a 3.6 million digit solution with the implication that an infinite length pattern had been determined. [N=2, 17, sum(1:17)=153]\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 challenge sequence shall step thru the steps and processing types to find Rokicki's result.\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 challenge is to find all solutions with lengths 1 thru 7.\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\u003eM=OddlyTri_1(N,Q) where N=digit length, Q=number of solutions, M is a vector of the Q values.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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