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 A196088 Positive integers a for which there is a (5/3)-Pythagorean triple (a,b,c) satisfying a<=b. 8

%I

%S 7,9,13,14,15,16,18,19,21,23,25,26,27,27,28,29,30,32,33,35,35,36,39,

%T 40,40,41,42,45,45,45,46,47,48,49,52,53,54,54,55,56,58,59,60,63,63,63,

%U 64,65,69,70,70,71,72,72,75,75,77,80,80,81,81,81,82,83,84,85,87

%N Positive integers a for which there is a (5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

%C See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

%t z8 = 600; z9 = 150; z7 = 100;

%t k = 5/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];

%t d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]

%t t[a_] := Table[d[a, b], {b, a, z8}]

%t u[n_] := Delete[t[n], Position[t[n], 0]]

%t Table[u[n], {n, 1, 15}]

%t t = Table[u[n], {n, 1, z8}];

%t Flatten[Position[t, {}]]

%t u = Flatten[Delete[t, Position[t, {}]]];

%t x[n_] := u[[3 n - 2]];

%t Table[x[n], {n, 1, z7}] (* A196088 *)

%t y[n_] := u[[3 n - 1]];

%t Table[y[n], {n, 1, z7}] (* A196089 *)

%t z[n_] := u[[3 n]];

%t Table[z[n], {n, 1, z7}] (* A196090 *)

%t x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]

%t y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]

%t z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]

%t f = Table[x1[n], {n, 1, z9}];

%t x2 = Delete[f, Position[f, 0]] (* A196091 *)

%t g = Table[y1[n], {n, 1, z9}];

%t y2 = Delete[g, Position[g, 0]] (* A196092 *)

%t h = Table[z1[n], {n, 1, z9}];

%t z2 = Delete[h, Position[h, 0]] (* A196093 *)

%Y Cf. A195770, A196089, A196090, A196091.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 27 2011

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)