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A196112 Positive integers a for which there is a 3-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196112 #9 Mar 30 2012 18:57:49
%S A196112 3,5,6,7,8,9,9,10,11,11,12,13,13,14,15,15,15,16,16,17,17,18,18,19,19,
%T A196112 20,21,21,21,21,21,22,22,23,23,24,24,24,25,25,26,26,27,27,27,27,28,29,
%U A196112 30,30,30,31,32,32,32,33,33,33,33,33,34,34,35,35,36,36,37,38,38
%N A196112 Positive integers a for which there is a 3-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196112 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196112 z8 = 900; z9 = 250; z7 = 200;
%t A196112 k = 7/4; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196112 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196112 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196112 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196112 Table[u[n], {n, 1, 15}]
%t A196112 t = Table[u[n], {n, 1, z8}];
%t A196112 Flatten[Position[t, {}]]
%t A196112 u = Flatten[Delete[t, Position[t, {}]]];
%t A196112 x[n_] := u[[3 n - 2]];
%t A196112 Table[x[n], {n, 1, z7}]  (* A196105 *)
%t A196112 y[n_] := u[[3 n - 1]];
%t A196112 Table[y[n], {n, 1, z7}]  (* A196106 *)
%t A196112 z[n_] := u[[3 n]];
%t A196112 Table[z[n], {n, 1, z7}]  (* A196107 *)
%t A196112 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196112 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196112 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196112 f = Table[x1[n], {n, 1, z9}];
%t A196112 x2 = Delete[f, Position[f, 0]]  (* A196108 *)
%t A196112 g = Table[y1[n], {n, 1, z9}];
%t A196112 y2 = Delete[g, Position[g, 0]]  (* A196109 *)
%t A196112 h = Table[z1[n], {n, 1, z9}];
%t A196112 z2 = Delete[h, Position[h, 0]]  (* A196110 *)
%Y A196112 Cf. A195770, A196113, A196114, A196115.
%K A196112 nonn
%O A196112 1,1
%A A196112 _Clark Kimberling_, Sep 28 2011