

One form of   Pythagorean quadruples   is   (for positive integers   a,   b,   c,   and   d):



    a2   +   b2   +   c2     =     d2 


An example:

    22   +   32   +   62     =     72 
 which is:
    4    +   9    +   36     =     49 


Task

For positive integers up   2,200   (inclusive),   for all values of   a,  
b,   c,   and   d,

find   (and show here)   those values of   d   that   can't   be represented.

Show the values of   d   on one line of output   (optionally with a title).



Related tasks

   Euler's sum of powers conjecture. 
   Pythagorean triples.


Reference

   the Wikipedia article:   Pythagorean quadruple.


powersOfTwo :: [Int]
powersOfTwo = iterate (2 *) 1
 
unrepresentable :: [Int]
unrepresentable = merge powersOfTwo ((5 *) <$> powersOfTwo)
 
merge :: [Int] -> [Int] -> [Int]
merge xxs@(x:xs) yys@(y:ys)
  | x < y = x : merge xs yys
  | otherwise = y : merge xxs ys
 
main :: IO ()
main = do
  putStrLn "The values of d <= 2200 which can't be represented."
  print $ takeWhile (<= 2200) unrepresentable