

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.


# Project : Pythagorean quadruples
 
limit = 2200
pq = list(limit)
for n = 1 to limit
      for m = 1 to limit
           for p = 1 to limit
                 for x = 1 to limit
                       if pow(x,2) = pow(n,2) + pow(m,2) + pow(p,2)
                          pq[x] = 1
                       ok
                 next
           next
      next
next
pqstr = ""
for d = 1 to limit
      if pq[d] = 0
         pqstr = pqstr + d + " "
      ok
next
see pqstr + nl
 