A196169 Positive integers a for which there is a 7-Pythagorean triple (a,b,c) satisfying a<=b (includes multiplicities).

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..79.

Mathematica

z8 = 900; z9 = 250; z7 = 200;
k = 7; 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}]  (* A196169 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196170 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196171 *)
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]]  (* A196172 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196173 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196174 *)

Crossrefs

Cf. A195770, A196170, A196171, A196172, A196173, A196174.

Sequence in context: A270362 A196383 A074198 * A330561 A048688 A092695

Adjacent sequences: A196166 A196167 A196168 * A196170 A196171 A196172

Keyword

nonn

Author

Clark Kimberling, Sep 29 2011

Status

approved