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A196026 Positive integers a for which there is a (5/2)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196026 #8 Mar 30 2012 18:57:49
%S A196026 5,6,7,9,10,11,12,13,14,14,15,16,17,18,18,19,20,21,21,22,22,23,24,25,
%T A196026 25,25,26,26,27,28,28,29,30,30,30,31,32,32,33,34,34,35,35,35,36,36,37,
%U A196026 38,38,38,39,40,41,42,42,42,43,44,44,45,45,46,46,47,48,48,48,49
%N A196026 Positive integers a for which there is a (5/2)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196026 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196026 z8 = 800; z9 = 150; z7 = 100;
%t A196026 k = 5/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196026 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196026 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196026 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196026 Table[u[n], {n, 1, 15}]
%t A196026 t = Table[u[n], {n, 1, z8}];
%t A196026 Flatten[Position[t, {}]]
%t A196026 u = Flatten[Delete[t, Position[t, {}]]];
%t A196026 x[n_] := u[[3 n - 2]];
%t A196026 Table[x[n], {n, 1, z7}]   (* A196026 *)
%t A196026 y[n_] := u[[3 n - 1]];
%t A196026 Table[y[n], {n, 1, z7}]   (* A196027 *)
%t A196026 z[n_] := u[[3 n]];
%t A196026 Table[z[n], {n, 1, z7}]   (* A196028 *)
%t A196026 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196026 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196026 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196026 f = Table[x1[n], {n, 1, z9}];
%t A196026 x2 = Delete[f, Position[f, 0]]   (* A196029 *)
%t A196026 g = Table[y1[n], {n, 1, z9}];
%t A196026 y2 = Delete[g, Position[g, 0]]   (* A196030 *)
%t A196026 h = Table[z1[n], {n, 1, z9}];
%t A196026 z2 = Delete[h, Position[h, 0]]   (* A196031 *)
%Y A196026 Cf. A195770, A196027, A106028, A196029.
%K A196026 nonn
%O A196026 1,1
%A A196026 _Clark Kimberling_, Sep 26 2011