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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:...

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Easy Sequences 20: Counting Prime-sided Rectangles

A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-...

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Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area

A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-...

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Easy Sequences 17: Mu Variant Function

The mobius function is an important arithmetic function. It is often represented by the Greek letter mu (μ), and is sometimes ca...

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Easy Sequences 15: Pythagorean Area with maximum Hypotenuse

A pythagorean triangle is defined as a right triangle with all three sides having integer lengths. Examples of pythogorean trian...

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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...

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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...

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Easy Sequences 34: Modified Pascal's Triangle

Consider the integer triangle below: It follows the same ...

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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...

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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...

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Easy Sequences 26: Prime-Integer Line Segments

At the first quadrant in the -plane, you are asked to construct a line segment with the following specifications: Select a prim...

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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 ...

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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 ...

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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 any number ...

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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: ...

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Easy Sequences 24: Number of Coprime Lattice Points

Given a number 'n', you were tasked to mark and count all coprime lattice points at the first quadrant bounded by the points (0,...

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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...

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Easy Sequences 18: Set Bits of Triple Summations

The function S(n) is defined by the following triple summations: The double brackets mean that th...

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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...

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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). ...

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Easy Sequences 13: Average Speed of Spaceship

A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ...

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Easy Sequences 12: 50th Prime

Write a function that outputs the th prime after a given number . For example, the th prime after is . NOTE: If itself is pr...

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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,...

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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...

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Easy Sequences 5: Project Euler Problem 1 - Again!

We are all familiar with Project Euler Problem 1. This time let's try it on bigger multiples and larger range. Find the sum of ...

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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...

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Easy Sequences 11: Factorial Digits without Trailing Zeros

Here is an easy one... It is not difficult to count the number of digits of the factorial of a given number. For example for 'n...

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Easy Sequences 4: Eliminate the Days of Confusion

If a date is written in purely numeric format some dates can be confusing, if we don't know the date format used. For example, "...

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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 ...

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Easy Sequences 2: Trigonometric function with integral input and output

The function 'F', defined as: , will always return an integer if the input is a natural number (in radian...

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