login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Positive integers a for which there is a (-3/2)-Pythagorean triple (a,b,c) satisfying a<=b.
7

%I #8 Mar 30 2012 18:57:48

%S 2,3,4,5,6,6,7,8,9,9,10,10,10,11,12,12,13,14,14,15,15,15,15,15,16,16,

%T 17,18,18,18,18,19,20,20,20,21,21,22,22,22,23,24,24,25,25,26,26,26,27,

%U 27,27,28,28,29,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,34

%N Positive integers a for which there is a (-3/2)-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 = 800; z9 = 400; z7 = 100;

%t k = -3/2; 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}] (* A195918 *)

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

%t Table[y[n], {n, 1, z7}] (* A195919 *)

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

%t Table[z[n], {n, 1, z7}] (* A195920 *)

%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]] (* A195921 *)

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

%t y2 = Delete[g, Position[g, 0]] (* A195922 *)

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

%t z2 = Delete[h, Position[h, 0]] (* A195923 *)

%Y Cf. A195770, A195919, A195920, A195921.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 26 2011