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A196088 Positive integers a for which there is a (5/3)-Pythagorean triple (a,b,c) satisfying a<=b. 8
7, 9, 13, 14, 15, 16, 18, 19, 21, 23, 25, 26, 27, 27, 28, 29, 30, 32, 33, 35, 35, 36, 39, 40, 40, 41, 42, 45, 45, 45, 46, 47, 48, 49, 52, 53, 54, 54, 55, 56, 58, 59, 60, 63, 63, 63, 64, 65, 69, 70, 70, 71, 72, 72, 75, 75, 77, 80, 80, 81, 81, 81, 82, 83, 84, 85, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..67.

MATHEMATICA

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

k = 5/3; 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}]   (* A196088 *)

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

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

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

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

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]]  (* A196091 *)

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

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

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

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

CROSSREFS

Cf. A195770, A196089, A196090, A196091.

Sequence in context: A161892 A056528 A055565 * A066498 A102306 A066962

Adjacent sequences:  A196085 A196086 A196087 * A196089 A196090 A196091

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 27 2011

STATUS

approved

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Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)