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Determine whether a number is a Gaussian prime
A Gaussian prime is a number that cannot be factored. For example, is not a Gaussian prime because it can be factored as the p...

2 years ago

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Determine whether a number is a Zeisel number
Do you know what is interesting about the number 1729? That’s right: it’s the third Zeisel number, a number given by , where ...

2 years ago

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Compute the bubble popper fidget spinner sequence
A fidget spinner is a toy made of multiple lobes that pivot on a ball bearing. In some, the lobes hold bubble poppers, or rubber...

2 years ago

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Compute the Sisyphus sequence
A recent article in the New York Times featured the Online Encyclopedia of Integer Sequences, founded by Neil J.A. Sloane. One o...

2 years ago

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Factor a number into Fermi-Dirac primes
Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As note...

2 years ago

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List the Fermi-Dirac primes
The Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4,...

2 years ago

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List numbers such that every sum of consecutive positive integers ending in those numbers is composite
The sequence in question in this problem involves numbers such that all sums of consecutive positive integers ending with are ...

2 years ago

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Identify de Polignac numbers
The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, whi...

2 years ago

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List the two-bit primes
Each year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the New York Times. This year’s e...

2 years ago

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Solve an equation involving primes and fractions
Write a function to find pairs of primes and satisfying the equation where is an integer. The function should take a numbe...

2 years ago

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List the semiprimes
A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers and are semiprimes, but and are not....

2 years ago

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List odd twin composites
Twin primes, or prime numbers that differ by 2 (e.g., 17 and 19, 59 and 61, or 191 and 193), are the subject of several Cody pro...

2 years ago

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List the Euclid numbers
Euclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set , , . Comp...

2 years ago

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List the Beatriz numbers
Write a function to find integers less than or equal to an input value that solve the equation . The function gives the sum o...

2 years ago

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Compute the largest number whose prime factors sum to n
This problem deals with a sequence whose tenth term is 36 because the prime factors of 36 (2, 2, 3, 3) sum to 10. The number 32 ...

2 years ago

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List the Moran numbers
The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 ...

2 years ago

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Solve the arithmetic differential equation D(n) = n

2 years ago

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Compute the arithmetic derivative of integers

2 years ago

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List composite numbers that cannot be written as the sum of two primes

2 years ago

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Find pairs of primes with the same digit sum and a specified separation

2 years ago

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Identify prime words

2 years ago

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Play Outside In with primes
In the word game Outside In,* you start with a word, take the first and last letters, try to think of a word in which the two le...

2 years ago

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Count the primes in Collatz sequences
Several Cody problems (21, 69, 42937, 44448, 44784, 52422) involve Collatz sequences. These start with a seed . If is odd, the ...

2 years ago

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Determine whether a number is unprimeable
The number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprim...

2 years ago

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List prime anagrams of a number

2 years ago

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Find the smallest prime with n inside
Consider the sequence that begins 101, 113, 127, 131, 149, 151, 163,... Not only is every term prime, the th term is the smalles...

2 years ago

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List the nth prime quartet prefix
Prime numbers larger than 5 can end only in 1, 3, 7, or 9, but of course not all numbers ending in these four digits are prime. ...

2 years ago

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List Honaker primes
The number 131 is the 32nd prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digit...

2 years ago

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Label primes with the Erdos-Selfridge classification

2 years ago

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List Proth primes

2 years ago