

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.


# Emit a proof that the input is a pythagorean quad, or else false
def is_pythagorean_quad:
  . as $d
  | (.*.) as $d2
  | first(
      label $continue_a | range(1; $d) | . as $a | (.*.) as $a2
    |   if 3*$a2 > $d2 then break $continue_a else . end
    | label $continue_b | range($a; $d) | . as $b | (.*.) as $b2
    |   if $a2  + 2 * $b2  > $d2 then break $continue_b else . end
    | (($d2-($a2+$b2)) | sqrt) as $c
    | if ($c | floor) == $c then [$a, $b, $c] else empty end )
  // false;
 
# The specific task:
 
[range(1; 2201) | select( is_pythagorean_quad | not )] | join(" ")