p045.py

# Steve Beal
# Project Euler problem 45 solution
# 8/14/15

# Triangle, pentagonal, and hexagonal numbers are generated by the following
# formulae:
# Triangle:   T_n = n(n+1)/2     1, 3, 6, 10, 15, ...
# Pentagonal: P_n = n(3n-1)/2    1, 5, 12, 22, 35, ...
# Hexagonal:  H_n = n(2n-1)      1, 6, 15, 28, 45, ...

# It can be verified that T_285 = P_165 = H_143 = 40755.

# Find the next triangle number that is also pentagonal and hexagonal.

from utils import triangular_gen, is_pentagonal, is_hexagonal

def next_tri_pent_hex(last_tph = None):

    t = triangular_gen()

    if last_tph:
        # fast-forward the generator to the start point
        y = 0
        while y < last_tph:
            y = next(t)

    while True:
        x = next(t)
        if is_pentagonal(x) and is_hexagonal(x):
            return x


print(next_tri_pent_hex(40755))