

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.


def quad(top=2200):
    r = [False] * top
    ab = [False] * (top * 2)**2
    for a in range(1, top):
        for b in range(a, top):
            ab[a * a + b * b] = True
    s = 3
    for c in range(1, top):
        s1, s, s2 = s, s + 2, s + 2
        for d in range(c + 1, top):
            if ab[s1]:
                r[d] = True
            s1 += s2
            s2 += 2
    return [i for i, val in enumerate(r) if not val and i]
 
if __name__ == '__main__':
    n = 2200
    print(f"Those values of d in 1..{n} that can't be represented: {quad(n)}")