cp's OEIS Frontend

A196105 Positive integers a for which there is a (7/4)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196105 #8 Mar 30 2012 18:57:49
%S A196105 9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,26,27,28,28,29,30,31,33,
%T A196105 34,34,35,36,36,37,38,39,40,42,42,42,43,44,44,44,45,46,47,48,50,51,52,
%U A196105 52,52,53,54,55,56,56,57,58,60,60,60,61,62,62,63,63,64,65,66,66
%N A196105 Positive integers a for which there is a (7/4)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196105 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196105 z8 = 900; z9 = 250; z7 = 200;
%t A196105 k = 7/4; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196105 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196105 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196105 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196105 Table[u[n], {n, 1, 15}]
%t A196105 t = Table[u[n], {n, 1, z8}];
%t A196105 Flatten[Position[t, {}]]
%t A196105 u = Flatten[Delete[t, Position[t, {}]]];
%t A196105 x[n_] := u[[3 n - 2]];
%t A196105 Table[x[n], {n, 1, z7}]  (* A196105 *)
%t A196105 y[n_] := u[[3 n - 1]];
%t A196105 Table[y[n], {n, 1, z7}]  (* A196106 *)
%t A196105 z[n_] := u[[3 n]];
%t A196105 Table[z[n], {n, 1, z7}]  (* A196107 *)
%t A196105 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196105 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196105 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196105 f = Table[x1[n], {n, 1, z9}];
%t A196105 x2 = Delete[f, Position[f, 0]]  (* A196108 *)
%t A196105 g = Table[y1[n], {n, 1, z9}];
%t A196105 y2 = Delete[g, Position[g, 0]]  (* A196109 *)
%t A196105 h = Table[z1[n], {n, 1, z9}];
%t A196105 z2 = Delete[h, Position[h, 0]]  (* A196110 *)
%Y A196105 Cf. A195770, A196106, A196107, A196108.
%K A196105 nonn
%O A196105 1,1
%A A196105 _Clark Kimberling_, Sep 28 2011