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A096910 Primitive Pythagorean Quadruples a^2+b^2+c^2=d^2, 0 gcd(a,b,c,d)=1, sorted by d, then c, then b; sequence gives d values.

%I A096910 #9 Feb 16 2025 08:32:54
%S A096910 3,7,9,9,11,11,13,15,15,17,17,19,19,19,21,21,21,21,23,23,23,25,25,27,
%T A096910 27,27,27,27,29,29,29,31,31,31,31,33,33,33,33,33,33,33,35,35,35,35,37,
%U A096910 37,37,37,39,39,39,39,39,39,41,41,41,41,41,43,43,43,43,43,43,45,45,45
%N A096910 Primitive Pythagorean Quadruples a^2+b^2+c^2=d^2, 0<a<=b<=c<=d, gcd(a,b,c,d)=1, sorted by d, then c, then b; sequence gives d values.
%C A096910 Sequence with repetitions removed is A005818. - _Ivan Neretin_, May 24 2015
%H A096910 Ivan Neretin, <a href="/A096910/b096910.txt">Table of n, a(n) for n = 1..10000</a>
%H A096910 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanQuadruple.html">Pythagorean Quadruple.</a>
%t A096910 mx = 50; res = {}; Do[If[GCD[b, c, d] > 1, Continue[]]; If[IntegerQ[a = Sqrt[d^2 - b^2 - c^2]] && a > 0 && a <= b, AppendTo[res, {a, b, c, d}]], {d, mx}, {c, d}, {b, c}]; res[[All, 4]] (* _Ivan Neretin_, May 24 2015 *)
%Y A096910 Cf. A096907, A096908, A096909 (other components of the quadruple), A046086, A046087, A020882 (Pythagorean triples ordered in a similar way).
%K A096910 nonn
%O A096910 1,1
%A A096910 _Ray Chandler_, Aug 15 2004