Problem 45: Triangular, pentagonal, and hexagonal
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.
Test
{{test}}Console output