Tim

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Compute the Sequence of the Day
A sequence starts with 1 and 2, and each subsequent term is the sum of the digits of the product of the previous two terms. As a...

2 days ago

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Easy Sequences 48: Prime Big Omega of Factorial Sequence
For an integer , the prime big omega function, , is defined as the total number prime factors of . So, if , since , therefore ....

25 days ago

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Easy Sequences 44: Finding the Smallest Number whose Cube is divisible by a Factorial
Given a integer , our goal is to find the smallest integer , such that divides . For example, for , , because , (since ), and ...

26 days ago

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Collect a set of candy wrappers
This past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) their many neighbors with their costumes in...

28 days ago

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Easy Sequences 47: Boxes with Prime Edges
This is related to problem "Easy Sequences 41: Boxes with Integer Edges". However, here we will be investigating a smaller-sized...

1 month ago

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Easy Sequences 45: Second Derivative of Inverse Polynomial Function
The inverse of a function, is the function , that reverses . That means that if , then . For example, the function to convert ce...

1 month ago

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Easy Sequences 42: Areas of Non-constructible Polygons
A constructible polygon is a regular polygon that can be constructed using only a compass and a straightedge. Amazingly, Gauss ...

1 month ago

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Easy Sequences 43: Least Common Fibonacci Number
The Fibonacci sequence is a series whose elements are numbers starting with and , and subsequent Fibonacci numbers are defined...

1 month ago

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Easy Sequences 38: Prime Number Delta
The Prime Number Theorem states that: where is the prime counting function (number of pri...

2 months ago

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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...

2 months ago

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Easy Sequences 41: Boxes with Integer Edges
For this problem, we are asked to write a function that will count the number of boxes with integer edges, that has the same giv...

2 months 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 months ago

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Easy Sequences 39: Perfect Squares in Pascal's Triangle
Consider the 2nd, 3rd and 4th diagonals of the Pascal's Triangle, shown highlighted below: ...

2 months ago

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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). ...

2 months ago

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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...

2 months ago

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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 ...

2 months ago

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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...

2 months 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: ...

2 months 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...

2 months ago

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Easy Sequences 36: Hyperbolic Lattice Points
The graph, shown below, of the hyperbola: , passes through four positive lattice points:. ...

2 months ago

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Easy Sequences 34: Modified Pascal's Triangle
Consider the integer triangle below: It follows the same ...

2 months ago

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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:...

2 months ago

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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 ...

2 months ago

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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...

2 months 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...

2 months 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...

2 months 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...

2 months 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 ...

2 months 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: ...

2 months 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...

2 months ago

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