499 B
499 B
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
| Name | Formula | Numbers |
|---|---|---|
| Triangle | T_{n} = n(n+1)/2 |
1, 3, 6, 10, 15, ... |
| Pentagonal | P_{n} = n(3n-1)/2 |
1, 5, 12, 22, 35, ... |
| Hexagonal | H_{n} = 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.