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

9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 33, 34, 34, 35, 36, 36, 37, 38, 39, 40, 42, 42, 42, 43, 44, 44, 44, 45, 46, 47, 48, 50, 51, 52, 52, 52, 53, 54, 55, 56, 56, 57, 58, 60, 60, 60, 61, 62, 62, 63, 63, 64, 65, 66, 66

Offset: 1

Author

Clark Kimberling, Sep 28 2011

Keywords

• nonn

Comments

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

Crossrefs

Cf. A195770, A196106, A196107, A196108.

Programs

Mathematica

z8 = 900; z9 = 250; z7 = 200;
k = 7/4; 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}]  (* A196105 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196106 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196107 *)
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]]  (* A196108 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196109 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196110 *)