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Triangular, pentagonal, and hexagonal
Problem 45
Published on 06 June 2003 at 06:00 pm [Server Time]
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.
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