Problem 45 - After 40755, what is the next triangle number that is also pentagonal and hexagonal?

링크

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.

python - ugly brute force

limit = 100000 T = set([x*(x+1)/2 for x in range(limit)]) P = set([x*(3*x-1)/2 for x in range(limit)]) def H(n): return n*(2*n-1) x = 144 while (H(x) not in T or H(x) not in P) and x < limit: x += 1 print x, H(x)