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**Content Feed**

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Easy Sequences 40: Quadratic Congruence

Quadratic Congruence is a modular equation of the form: . In this exercise you will be given a vector containing the coefficie...

3 days ago

Solved

Easy Sequences 16: Volume of Embedded Octahedron

An octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure). ...

10 days ago

Solved

Easy Sequences 30: Nearly Pythagorean Triangles

A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an integer-sided triangle whose square of the longest side, which we wi...

10 days ago

Solved

Easy Sequences 27: Product of Radicals of Integers

The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

11 days ago

Solved

List the cuban primes

The number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. Write a function to list the cuba...

11 days ago

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Easy Sequences 35: Cutting a donut to Semi-prime pieces

The figure below illustrates how a torus (donut shape) can be cut in pieces with only cuts: ...

14 days ago

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Easy Sequences 37: Natural Factorable Polynomials

A polynomial of the form: , for , is said to be natural factorable if it can be factored into products of first degree binomials...

14 days ago

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Easy Sequences 36: Hyperbolic Lattice Points

The graph, shown below, of the hyperbola: , passes through four positive lattice points:. ...

15 days ago

Solved

Easy Sequences 22: Sum of Proper Fractions

Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:...

16 days ago

Solved

Easy Sequences 28: Sum of Radicals of Integers

The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

17 days ago

Solved

Easy Sequences 29: Odd proper divisors of odd proper divisors

The number is special. It has odd number of proper divisors: . Furthermore, if you take any of its proper divisors, say , it t...

17 days ago

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Easy Sequences 33: Web Trapped Ant

An ant is trapped on a spider web inside a can with open top. The can has a radius and height . A spider sitting on the outside...

18 days ago

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List modest numbers up to n

After determining the nude numbers, or the numbers that openly display some of their divisors as their digits, one would think t...

23 days ago

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Easy Sequences 21: Combinatorial Summations

Create the function S(n), defined by the following summation: The symbol is the combination f...

23 days ago

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Easy Sequences 31: N-N's Sequence

We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein a appears ...

23 days ago

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Easy Sequences 25: Product of Series

The function 'P(n)' is defined as the series product: where 'T(n)' is the triangular sum: ...

26 days ago

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Easy Sequences 23: Hat Guessing Game!

Consider the following Game Show: Hats, with numbers written on each, were placed on the heads of the participants. Participant...

26 days ago

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Multiply binary numbers

Write a function to multiply two binary numbers input as strings. For example, input values of ‘1011’ and ‘101’ should give ’110...

27 days ago

Solved

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 ...

1 month ago

Solved

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 ...

1 month ago

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Easy Sequences 6: Coefficient sums of derivatives

Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respecti...

2 months ago

Solved

Determine whether a number is a fibodiv number

The number 14 is a fibodiv number because you can divide it into 1 and 4, use those numbers as the seeds for a Fibonacci sequenc...

2 months ago

Solved

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 months ago

Solved

Count the ways to draw non-intersecting chords between points on a circle

There are 9 ways to draw non-intersecting chords between four points on the perimeter of a circle (including no chords at all). ...

2 months ago

Solved

Find the nth nude number

The number 672 is a nude number because it openly displays three of its divisors: 6, 7, and 2. In other words, a nude number is ...

2 months ago

Solved

Easy Sequences 9: Faithful Pairs

A "faithful number" is a non-prime number that is one less or one more than some prime number but not both. For example, for num...

2 months ago

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Easy Sequences 10: Sum of Cumsums of Fibonacci Sequence

The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F,...

2 months ago

Solved

Easy Sequences 8: Triangles with integer sides and prime perimeters

The triangle below is special. It has integer sides and a prime perimeter. Given an integer "n" we want to know how many t...

2 months ago

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Hoax Numbers

A Hoax Number (OEIS A019506) is defined as a composite number, whose sum of digits is equal to the sum of digits of its distinct...

2 months ago

Solved

Easy Sequences 3: Prime 44-number Squares

The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd ...

2 months ago