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Search for seesaw primes
Cody Problem 60958 introduced seesaw numbers. A number is a seesaw number if the next smaller numbers can be placed on a seesa...

12 days ago

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List mean-of-2 primes
The prime number 53 is the average of the first prime before it (47) and the first prime after it (59), and the prime number 11 ...

12 days ago

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Compile evidence for the Carmichael totient conjecture
The totient function counts the positive integers up to that are relatively prime to . The Carmichael totient conjecture state...

12 days ago

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Intersect three sequences
Most numbers have interesting properties, if you look hard enough and interpret “interesting” liberally. Let’s choose a number a...

12 days ago

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Find the closest e-abundant numbers
An abundant number is an integer whose sum of its positive proper divisors—or the sum of its divisors excluding itself—exceeds ...

12 days ago

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List e-perfect numbers
A perfect number is an integer that equals the sum of its positive proper divisors—or the sum of its divisors excluding itself. ...

12 days ago

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Sum powers of e-divisors
In number theory the function produces the sum of divisors of an integer raised to the power . Setting sums the divisors, as ...

12 days ago

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Count the e-divisors of an integer
Cody Problem 2664 asks us to count the divisors of an integer, and Cody Problem 60843 involves listing the e-divisors of an inte...

12 days ago

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Determine the e-divisors of an integer
From MathWorld: is called an e-divisor (or exponential divisor) of a number with prime factorization if and where for...

12 days ago

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List the notes of a major scale
If you have seen The Sound of Music, then you are familiar with the major scale: do, re, mi, fa, sol, la, ti, do. The C major sc...

12 days ago

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Construct the number counts sequence
A sequence is constructed in the following way. The zeroth term is 1, and the next terms are determined by counting the number i...

12 days ago

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List the first of three consecutive square-free numbers
The numbers 13, 14, and 15 are consecutive, of course, but they also share the property of being square-free. That is, each numb...

12 days ago

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Count the primes resulting from changing one digit of a number
If you start with the number 24 and seek primes by changing a single digit, you can find two: 23 and 29. If you start with 130, ...

12 days ago

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Solve an easy binary puzzle
A binary puzzle presents a square grid (or matrix) of cells in which each cell must be 0 or 1. The finished puzzle must follow t...

12 days ago

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Convert integers from base 10 to proper primary notation
This problem is the companion to Cody Problem 60782. The proper primary system of expressing non-negative numbers has three digi...

12 days ago

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Identify points inside a Reuleaux triangle
Write a function to identify points that lie in or on a Realeaux triangle, which is a curve of constant width. The input to the ...

12 days ago

Solved

Determine whether a number is a Ludic prime
Ludic numbers are formed by a sieve. Start with a list of the positive integers. Skip 1 and start with 2. Then delete every seco...

12 days ago

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Find the closest canyon prime
My wife and I celebrated our honeymoon and most recent anniversary in Yellowstone and Grand Teton National Parks. After returnin...

12 days ago

Solved

Extend the digamma function to negative arguments
While solving one of Ramon Villamangca’s problems, I needed the value of , where is the digamma function. However, MATLAB’s fun...

12 days ago

Solved

Sum the reciprocals of polygonal numbers
As explained in Cody Problem 60571, a polygonal number is the number of dots arranged in the shape of a regular polygon. For exa...

12 days ago

Solved

Compute the totient summatory function
Cody Problem 656 deals with the totient function, denoted by which counts the numbers less than that are relatively prime to ....

12 days ago

Solved

Compute a sequence with the whyphi sieve
A few problems on Cody involve sieving. For example, Cody Problem 45367 involves the famous Sieve of Eratosthenes. CP 50811 uses...

12 days ago

Solved

Alert a city about a spill
Problem statement Cody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any muni...

12 days ago

Solved

Travel a path
In Cody Problem 60251, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, ...

12 days ago

Solved

Compute the Ramanujan tau function
The Ramanujan tau function is defined by the relation where . The first few values of are 1, -24, 252, -1472, and 4830. W...

12 days ago

Solved

List the segmented numbers
The sequence of segmented numbers begins 1, 2, 4, 5, 8, 10, 14, 15, 16. Notice that none of the terms is the sum of consecutive ...

12 days ago

Solved

List the ways to write 1/n as the sum of two unit fractions
Cody Problem 59841 involved counting the ways that can be written as the sum of two unit fractions (those with a numerator of 1...

12 days ago

Solved

Count the ways to write 1/n as the sum of two unit fractions
The number 1/2 can be written as 1/3+1/6 and 1/4+1/4, and the number 1/9 can be written as 1/18+1/18, 1/12+1/36, and 1/10+1/90. ...

12 days ago

Solved

Solve an ODE: Ekman spiral on a solid surface
Problem Write a function to solve for and as a function of in this system of ordinary differential equations: where , ...

12 days ago

Solved

Update course numbers and abbreviations
Suppose that the educational institution where you teach purchases new software to handle many essential functions, including co...

13 days ago