CntSquareness.hs

-- n is a square number or not
isSquare:: Int -> Bool
isSquare n = t*t == n
  where t = round(sqrt (fromIntegral(n)))

-- "n = c*c + (n-c*c)" is square split or not
isSquareSplit:: Int -> Int -> Bool
isSquareSplit n c = isSquare (n - c*c)

-- return whether n is splittable as two square number or not
splittableAsSquare:: Int -> Bool
splittableAsSquare n = True `elem` map (\c -> isSquareSplit (fromIntegral n) c) [1 .. t]
  where t = round(sqrt (fromIntegral(n)))

cntSplitAndNot:: Int -> Int
cntSplitAndNot n
  |(splittableAsSquare(n) == False) = 0
  |(otherwise) = 1 + (length (takeWhile (\c -> not(splittableAsSquare(c))) [n+1 ..]))

moreThanCntSplitAndNotFrom:: Int -> Int -> Int
moreThanCntSplitAndNotFrom s k = head(filter (\n -> cntSplitAndNot n >= k) [s ..])

moreThanCntSplitAndNot:: Int -> Int
moreThanCntSplitAndNot k = moreThanCntSplitAndNotFrom 1 k