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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A196119 Positive integers a for which there is a 4-Pythagorean triple (a,b,c) satisfying a<=b. 7
3, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 28, 28, 28, 28, 29, 30, 30, 30, 31, 32 (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 = 900; z9 = 250; z7 = 200;

k = 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}]  (* A196119 *)

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

Table[y[n], {n, 1, z7}]  (* A196120 *)

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

Table[z[n], {n, 1, z7}]  (* A196121 *)

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]]  (* A196122 *)

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

y2 = Delete[g, Position[g, 0]]  (* A196123 *)

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

z2 = Delete[h, Position[h, 0]]  (* A196124 *)

CROSSREFS

Cf. A195770, A196120, A196121, A196122.

Sequence in context: A225179 A121857 A121854 * A225852 A198458 A134483

Adjacent sequences:  A196116 A196117 A196118 * A196120 A196121 A196122

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 28 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 06:30 EST 2016. Contains 278749 sequences.