OFFSET
1,2
COMMENTS
See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
EXAMPLE
MATHEMATICA
z8 = 800; z9 = 400; z7 = 100;
k = -1/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}] (* A195872 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}] (* A195873 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}] (* A195874 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]] (* A195875 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]] (* A195876 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]] (* A195877 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 25 2011
STATUS
approved