Primitive Pythagorean quadruples (d, c, b, a) sorted so that a <= b <= c < d.
3, 2, 2, 1, 7, 6, 3, 2, 9, 7, 4, 4, 9, 8, 4, 1, 11, 7, 6, 6, 11, 9, 6, 2, 13, 12, 4, 3, 15, 11, 10, 2, 15, 14, 5, 2, 17, 12, 9, 8, 17, 12, 12, 1, 19, 15, 10, 6, 19, 17, 6, 6, 19, 18, 6, 1, 21, 16, 11, 8, 21, 16, 13, 4, 21, 19, 8, 4, 21, 20, 5, 4, 23, 18, 13, 6
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Quadruples such that d^2 = c^2 + b^2 + a^2. There are only a finite number of cases that sum to a given d^2. Only odd values of d appear.
T. D. Noe, Plot of 1000 quadruples
T. D. Noe, Table of 1000 quadruples
Eric W. Weisstein, MathWorld: Pythagorean Quadruple
Wikipedia, Pythagorean quadruple
(Mma) nn = 400; t4 = {}; Do[If[GCD[a, b, c] == 1 && IntegerQ[Sqrt[a^2 + b^2 + c^2]], d = Sqrt[a^2 + b^2 + c^2]; AppendTo[t4, {a, b, c, d}]], {a, nn}, {b, a, nn}, {c, b, nn}]; t4a = Sort[Reverse /@ Select[t4, #[[4]] <= 200 &]]; t4a = Take[t4a, 1000];
Cf. A263728 (three-dimensional case), S001062-S001069.
nonn,tabl
T. D. Noe, Aug 07 2017