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Triangular, pentagonal, and hexagonal

Problem 45

Published on Friday, 6th June 2003, 06:00 pm; Solved by 36939

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.