Project Euler #45

euler45.py

from math import sqrt
from itertools import islice
from itertools import count

def pentagonal(n):
    return not ((sqrt(24 * n + 1) + 1) / 6) % 1

def hexagonal(n):
    return not ((sqrt(8 * n + 1) + 1) / 4) % 1

def triangle(n):
    return ((n + 1) * n) / 2

print islice((triangle(n) for n in count(285 + 1)
                if pentagonal(triangle(n))
                    and hexagonal(triangle(n))), 1).next()