

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.


package main
 
import "fmt"
 
const (
    N = 2200
    N2 = N * N * 2
)
 
func main() {
    s  := 3 
    var s1, s2 int    
    var r  [N + 1]bool
    var ab [N2 + 1]bool
 
    for a := 1; a <= N; a++ {
        a2 := a * a
        for b := a; b <= N; b++ {
            ab[a2 + b * b] = true
        }
    }
 
    for c := 1; c <= N; c++ {
        s1 = s
        s += 2
        s2 = s
        for d := c + 1; d <= N; d++ {
            if ab[s1] {
                r[d] = true
            }
            s1 += s2
            s2 += 2
        }
    }
 
    for d := 1; d <= N; d++ {
        if !r[d] {
            fmt.Printf("%d ", d)
        }       
    }
    fmt.Println()
}