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A196033 Positive integers a for which there is a (-4/3)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196033 #12 May 15 2017 16:06:46
%S A196033 3,4,5,6,7,8,8,9,9,10,11,12,12,13,14,15,15,16,16,16,17,18,18,19,20,20,
%T A196033 21,21,21,22,23,24,24,24,24,25,26,27,27,27,27,28,28,28,28,29,30,30,31,
%U A196033 32,32,32,32,33,33,33,34,35,35,35,36,36,36,36,36,36,37,38,39
%N A196033 Positive integers a for which there is a (-4/3)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196033 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196033 z8 = 800; z9 = 200; z7 = 200;
%t A196033 k = -4/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196033 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196033 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196033 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196033 Table[u[n], {n, 1, 15}]
%t A196033 t = Table[u[n], {n, 1, z8}];
%t A196033 Flatten[Position[t, {}]]
%t A196033 u = Flatten[Delete[t, Position[t, {}]]];
%t A196033 x[n_] := u[[3 n - 2]];
%t A196033 Table[x[n], {n, 1, z7}]   (* A196033 *)
%t A196033 y[n_] := u[[3 n - 1]];
%t A196033 Table[y[n], {n, 1, z7}]   (* A196034 *)
%t A196033 z[n_] := u[[3 n]];
%t A196033 Table[z[n], {n, 1, z7}]   (* A196035 *)
%t A196033 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196033 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196033 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196033 f = Table[x1[n], {n, 1, z9}];
%t A196033 x2 = Delete[f, Position[f, 0]]   (* A196036 *)
%t A196033 g = Table[y1[n], {n, 1, z9}];
%t A196033 y2 = Delete[g, Position[g, 0]]   (* A196037 *)
%t A196033 h = Table[z1[n], {n, 1, z9}];
%t A196033 z2 = Delete[h, Position[h, 0]]   (* A196038 *)
%Y A196033 Cf. A195770, A196034, A196035, A196036.
%K A196033 nonn
%O A196033 1,1
%A A196033 _Clark Kimberling_, Sep 27 2011