

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.


my \N = 2200;
my @sq = (0 .. N)»²;
my @not = False xx N;
@not[0] = True;
 
(1 .. N).race.map: -> $d {
    my $last = 0;
    for $d ... ($d/3).ceiling -> $a {
        for 1 .. ($a/2).ceiling -> $b {
            last if (my $ab = @sq[$a] + @sq[$b]) > @sq[$d];
            if (@sq[$d] - $ab).sqrt.narrow ~~ Int {
                @not[$d] = True;
                $last = 1;
                last
            }
        }
        last if $last;
    }
}
 
say @not.grep( *.not, :k );