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(3n1)/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.
#integer_sqrt #triangles #pentagonals #is_pentagonal? #hexagonals #is_hexagonal? def p45 i=285 while true t=triangles(i+=1) if(is_pentagonal?(t) and is_hexagonal?(t)) puts t return end end end