-- 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.


-- 30s is kinda okay (not really)
main = do
    let triangle = [n * (n + 1) `div` 2 | n <- [1..]]
        pentagonal = [n * (3 * n - 1) `div` 2 | n <- [1..]]
        hexagonal = [n * (2 * n - 1) | n <- [1..]]
        isPentagonal n = n `elem` takeWhile (<= n) pentagonal
        isHexagonal n = n `elem` takeWhile (<= n) hexagonal
    print (take 2 [t | t <- drop 284 triangle, isPentagonal t, isHexagonal t])