problem044.py

'''
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 is pentagonal and D = |Pk - Pj| is minimised;

what is the value of D?
'''
from figurate_numbers import pentagonal
from figurate_numbers import is_pentagonal

pents = set()

i = 1
while i:
    n = pentagonal(i)
    for p in pents:
        d = n - p
        if d in pents and is_pentagonal(n + p):
            print d
            i = -1  # break
    pents.add(n)
    i += 1