#!/usr/bin/env python3

# Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:
#
# 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
#
# It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.
#
# Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk − Pj| is minimised;
# what is the value of D?

from projecteuler import is_pentagonal, timing


@timing
def p044() -> None:
    found = 0
    n = 2

    # Check all couples of pentagonal numbers until the right one
    # is found. Use the function implemented in projecteuler.py to
    # check if the sum and difference ot the two numbers is pentagonal.
    while not found:
        pn = n * (3 * n - 1) // 2

        for m in range(1, n):
            pm = m * (3 * m - 1) // 2

            if is_pentagonal(pn+pm) and is_pentagonal(pn-pm):
                found = 1
                break

        n = n + 1

    print('Project Euler, Problem 44')
    print(f'Answer: {pn - pm}')


if __name__ == '__main__':
    p044()