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Fibonacci Decomposition

Every positive integer has a unique decomposition into nonconsecutive Fibonacci numbers f1+f2+ ... Given a positive integer n, r...

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How many Fibonacci numbers?

Find the number of unique Fibonacci numbers (don't count repeats) in a vector of positive integers. Example: x = [1 2 3 4...

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Prime factor digits

Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...

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Get all prime factors

List the prime factors for the input number, in decreasing order. List each factor. If the prime factor occurs twice, list it as...

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Factorize THIS, buddy

List the prime factors for the input number, in decreasing order. List each factor only once, even if the factorization includes...

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The Goldbach Conjecture

The <http://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach conjecture> asserts that every even integer greater than 2 can ...

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Circular Primes (based on Project Euler, problem 35)

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. The...

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Largest Twin Primes

<http://en.wikipedia.org/wiki/Twin_prime Twin primes> are primes p1, p2 = p1 + 2 such that both p1 and p2 are prime numbers. Giv...

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Fibonacci-Sum of Squares

Given the Fibonacci sequence defined by the following recursive relation, * F(n) = F(n-1) + F(n-2) * where F(1) = 1 and F(1)...

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Mersenne Primes

A Mersenne prime is a prime number of the form M = 2^p - 1, where p is another prime number. For example, 31 is a Mersenne prim...

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Mersenne Primes vs. All Primes

A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. <https://www.mathworks.com/matl...

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Find nearest prime number less than input number

Find nearest prime number less than input number. For example: if the input number is 125, then the nearest prime number whi...

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Sophie Germain prime

In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prim...

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Find the next prime number

Find the next prime number or numbers for given n. For example: n = 1; out = 2; or n = [5 7]; out = [7 11]; ...

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Make a vector of prime numbers

Input(n) - length of vector with prime numbers Output(v) - vector of prime numbers Example: * n=1; v=2 * n=3; v=[2 3 5...

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Project Euler: Problem 5, Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smalle...

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Project Euler: Problem 6, Natural numbers, squares and sums.

The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ...

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Project Euler: Problem 7, Nth prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the Nth prime nu...

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Project Euler: Problem 9, Pythagorean numbers

A Pythagorean triplet is a set of three natural numbers, a b c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 =...

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Project Euler: Problem 1, Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23...

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Project Euler: Problem 10, Sum of Primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below the input, N. Thank you <http:/...

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Calculate Inner Product

Given two input matrices, |x| and |y|, check if their inner dimensions match. * If they match, create an output variable |z|...

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Find MPG of Lightest Cars

The file |cars.mat| contains a table named |cars| with variables |Model|, |MPG|, |Horsepower|, |Weight|, and |Acceleration| for ...

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Integer Sequence - II : New Fibonacci

Crack the following Integer Sequence. (Hints : It has been obtained from original Fibonacci Sequence and all the terms are also ...

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Find the next Fibonacci number

In the sequence of Fibonacci numbers, every number is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

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Return fibonacci sequence do not use loop and condition

Calculate the nth Fibonacci number. Given n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ... Examples: ...

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Return the Fibonacci Sequence

Write a code which returns the Fibonacci Sequence such that the largest value in the sequence is less than the input integer N. ...

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Project Euler: Problem 2, Sum of even Fibonacci

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 te...

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Number of Even Elements in Fibonacci Sequence

Find how many even Fibonacci numbers are available in the first d numbers. Consider the following first 14 numbers 1 1 2...

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