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Find Logic 30

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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 ...

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Find Logic 22

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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...

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Find Logic 21

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List primes of the form xy+z
Consider three consecutive integers , , and . When is the number prime? For example, if or , then the results are 17 and 37, ...

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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...

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Express numbers as the sum of a prime, a square, and a cube
While traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 m...

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Compute Khinchin's constant
Khinchin's constant K_0 = 2.684542001... (also written "Khintchine's constant") has the amazing property that it is the limiting...

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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...

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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...

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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,...

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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...

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List numbers such that every sum of consecutive positive integers ending in those numbers is not prime
The sequence in question in this problem involves numbers such that all sums of consecutive positive integers ending with are ...

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Compute a sum
Write a function to compute the following sum Although a solution is available for general values of the coefficients, the co...

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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...

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Find primes and integers that solve an equation
Write a function to find all primes and non-negative integers that solve the equation where is an integer. If there are no...

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Compute the area of a Q
A figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex...

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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....

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Integrate a power tower
Write a function to compute this integral where . That is, the integrand is (x to the x) to the (x to the x) to the (x to the...

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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...

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Integrate a product of gamma functions
Write a function to compute the following integral: where and is the gamma function, the subject of Cody Problem 46025.

3 months ago