

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.


 
import java.util.ArrayList;
import java.util.List;
 
public class PythagoreanQuadruples {
 
    public static void main(String[] args) {
        long d = 2200;
        System.out.printf("Values of d < %d where a, b, and c are non-zero and a^2 + b^2 + c^2 = d^2 has no solutions:%n%s%n", d, getPythagoreanQuadruples(d));
    }
 
    //  See:  https://oeis.org/A094958
    private static List<Long> getPythagoreanQuadruples(long max) {
        List<Long> list = new ArrayList<>();
        long n = -1;
        long m = -1;
        while ( true ) {
            long nTest = (long) Math.pow(2, n+1);
            long mTest = (long) (5L * Math.pow(2, m+1));
            long test = 0;
            if ( nTest > mTest ) {
                test = mTest;
                m++;
            }
            else {
                test = nTest;
                n++;
            }
            if ( test < max ) {
                list.add(test);
            }
            else {
                break;
            }
        }
        return list;
    }
 
}
 