Project Euler Problem 45 This is mostly unoptimized and terribly slow. Takes about 40 seconds on my i5-3320M.

pe_45.hs

-- Project Euler Problem 45
--
-- Triangle, pentagonal, hexagonal
--
-- 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.

main = print . head $ triPentHex

triPentHex :: [Integer]
triPentHex = filter isPentHex triangles
  where
    triangles   = dropWhile (<=40755) $ scanl1 (+) [1..]
    pentagonals = dropWhile (<=40755) $ scanl1 (+) [1,4..]
    hexagonals  = dropWhile (<=40755) $ scanl1 (+) [1,5..]
    elemOrdered ys x = elem x $ takeWhile (<=x) ys
    isPentHex x = (elemOrdered hexagonals x) && (elemOrdered pentagonals x)