

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

# It can be verified that T285 = P165 = H143 = 40755.

# Find the next triangle number that is also pentagonal and hexagonal.
from utils.common import triangle, is_pentagonal, is_hexagonal
for i in range(286, 100000):
	t = triangle(i)
	if is_pentagonal(t) and is_hexagonal(t):
		print(int(t))
		break
