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A195778 Positive integers a for which there is a (-1)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A195778 #6 Mar 30 2012 18:57:48
%S A195778 1,2,3,3,4,5,5,5,6,6,7,7,7,8,8,9,9,9,10,10,10,11,11,11,12,12,13,13,13,
%T A195778 14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,18,18,18,19,19,19,20,20,
%U A195778 20,21,21,21,21,21,22,22,22,23,23,23,24,24,24,24,24,25,25,25
%N A195778 Positive integers a for which there is a (-1)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A195778 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%e A195778 First five (-1)-Pythagorean triples (A195778):
%e A195778 (1,1,1), (2,2,2), (3,3,3), (3,8,7), (4,4,4).
%e A195778 First five primitive (-1)-Pythagorean triples (A195796):
%e A195778 (1,1,1), (3,8,7), (5,8,7), (5,21,19), (7,15,13).
%t A195778 z8 = 800; z9 = 400; z7 = 100;
%t A195778 k = -1; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A195778 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A195778 t[a_] := Table[d[a, b], {b, a, z8}]
%t A195778 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A195778 Table[u[n], {n, 1, 15}]
%t A195778 t = Table[u[n], {n, 1, z8}];
%t A195778 Flatten[Position[t, {}]]
%t A195778 u = Flatten[Delete[t, Position[t, {}]]];
%t A195778 x[n_] := u[[3 n - 2]];
%t A195778 Table[x[n], {n, 1, z7}]  (* A195778 *)
%t A195778 y[n_] := u[[3 n - 1]];
%t A195778 Table[y[n], {n, 1, z7}]  (* A195794 *)
%t A195778 z[n_] := u[[3 n]];
%t A195778 Table[z[n], {n, 1, z7}]  (* A195795 *)
%t A195778 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A195778 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A195778 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A195778 f = Table[x1[n], {n, 1, z9}];
%t A195778 x2 = Delete[f, Position[f, 0]] (* A195796 *)
%t A195778 g = Table[y1[n], {n, 1, z9}];
%t A195778 y2 = Delete[g, Position[g, 0]] (* A195862 *)
%t A195778 h = Table[z1[n], {n, 1, z9}];
%t A195778 z2 = Delete[h, Position[h, 0]] (* A195863 *)
%Y A195778 Cf. A195770, A009004, A195794, A195795, A195796, A195862, A195863.
%K A195778 nonn
%O A195778 1,2
%A A195778 _Clark Kimberling_, Sep 25 2011