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A196369 Positive integers a for which there is a (-3)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196369 #8 Mar 30 2012 18:57:49
%S A196369 1,2,3,3,3,4,5,5,6,6,6,7,7,7,8,8,8,9,9,9,9,9,10,10,11,11,11,12,12,12,
%T A196369 13,13,13,14,14,14,15,15,15,15,15,15,16,16,16,16,16,17,17,17,18,18,18,
%U A196369 18,18,19,19,19,20,20,21,21,21,21,21,21,21,21,21,22,22,22,23,23
%N A196369 Positive integers a for which there is a (-3)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196369 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196369 z8 = 900; z9 = 250; z7 = 200;
%t A196369 pIntegerQ := IntegerQ[#1] && #1 > 0 &;
%t A196369 k = -3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196369 d[a_, b_] := If[pIntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196369 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196369 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196369 Table[u[n], {n, 1, 15}]
%t A196369 t = Table[u[n], {n, 1, z8}];
%t A196369 Flatten[Position[t, {}]]
%t A196369 u = Flatten[Delete[t, Position[t, {}]]];
%t A196369 x[n_] := u[[3 n - 2]];
%t A196369 Table[x[n], {n, 1, z7}]  (* A196369 *)
%t A196369 y[n_] := u[[3 n - 1]];
%t A196369 Table[y[n], {n, 1, z7}]  (* A196370 *)
%t A196369 z[n_] := u[[3 n]];
%t A196369 Table[z[n], {n, 1, z7}]  (* A196371 *)
%t A196369 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196369 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196369 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196369 f = Table[x1[n], {n, 1, z9}];
%t A196369 x2 = Delete[f, Position[f, 0]]  (* A196372 *)
%t A196369 g = Table[y1[n], {n, 1, z9}];
%t A196369 y2 = Delete[g, Position[g, 0]]  (* A196373 *)
%t A196369 h = Table[z1[n], {n, 1, z9}];
%t A196369 z2 = Delete[h, Position[h, 0]]  (* A196374 *)
%Y A196369 Cf. A195770, A196370, A196371, A196372.
%K A196369 nonn
%O A196369 1,2
%A A196369 _Clark Kimberling_, Oct 01 2011