Triangular, pentagonal, and hexagonal
Problem 45
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
It can be verified that T285 = P165 = H143 = 40755.
Find the next triangle number that is also pentagonal and hexagonal.
from math import sqrt
def run():
# 100000 found by trial and error
for x in range(40756, 100000):
c = (x**2 + x) / 2
y = (0.5 + sqrt(0.25 + 6 * c)) / 3
z = (1 + sqrt(1 + 8 * c)) / 4
if y - int(y) == 0 and z - int(z) == 0:
return (x**2 + x) / 2