

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.


(de quadruples (N)
   (let (AB NIL  S 3  R)
      (for A N
         (for (B A (>= N B) (inc B))
            (idx
               'AB
               (+ (* A A) (* B B))
               T ) ) )
      (for C N
         (let (S1 S  S2)
            (inc 'S 2)
            (setq S2 S)
            (for (D (+ C 1) (>= N D) (inc D))
               (and (idx 'AB S1) (idx 'R D T))
               (inc 'S1 S2)
               (inc 'S2 2) ) ) )
      (make
         (for A N
            (or (idx 'R A) (link A)) ) ) ) )
 
(println (quadruples 2200))