project euler

Quadratic primes.

Euler discovered the remarkable quadratic formula:

n² + n + 41

»

Reciprocal cycles.

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2  =  0.5
1/3  =  0.(3)
1/4  =  0.25
1/5  =  0.2
1/6  =  0.1(6)
1/7  =  0.(142857)
1/8  =  0.125
1/9  =  0.(1)
1/10 =  0.1

»

1000-digit Fibonacci number.

The Fibonacci sequence is defined by the recurrence relation:
F(n) = F(n−1) + F(n−2), where F(1) = 1 and F(2) = 1.

»

Lexicographic permutations.

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic...

Non-abundant sums.

A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.

Names scores. Using names.txt (right click and ‘Save Link/Target As…’), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value...