Triangular, pentagonal, and hexagonal
Problem 45
Published on Friday, 6th June 2003, 06:00 pm; Solved by 33631Triangle, 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(2n1) |
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.