login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195939 Positive integers a for which there is a (1/3)-Pythagorean triple (a,b,c) satisfying a<=b. 8
3, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 13, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 24, 24, 24, 25, 25, 26, 27, 27, 27, 27, 27, 27, 28, 29, 30, 30, 30, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 34, 35, 35, 35, 36, 36 (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..70.

MATHEMATICA

z8 = 800; z9 = 400; z7 = 100;

k = 1/3; 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}]  (* A195939 *)

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

Table[y[n], {n, 1, z7}]  (* A195940 *)

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

Table[z[n], {n, 1, z7}]  (* A195941 *)

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]] (* A195990 *)

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

y2 = Delete[g, Position[g, 0]] (* A195991 *)

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

z2 = Delete[h, Position[h, 0]] (* A195992 *)

CROSSREFS

Cf. A195770, A195940, A195941, A195990.

Sequence in context: A272756 A322350 A205560 * A317587 A235647 A010616

Adjacent sequences:  A195936 A195937 A195938 * A195940 A195941 A195942

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 26 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 22 07:17 EDT 2019. Contains 326172 sequences. (Running on oeis4.)