A103606 Primitive Pythagorean triples in nondecreasing order of perimeter, with each triple in increasing order, and if perimeters coincide then increasing order of the even members.

3, 4, 5, 5, 12, 13, 8, 15, 17, 7, 24, 25, 20, 21, 29, 12, 35, 37, 9, 40, 41, 28, 45, 53, 11, 60, 61, 16, 63, 65, 33, 56, 65, 48, 55, 73, 13, 84, 85, 36, 77, 85, 39, 80, 89, 20, 99, 101, 65, 72, 97

Offset: 1

Author

Alexandre Wajnberg, Mar 24 2005

Keywords

• easy
• nonn
• tabf

Comments

The NAME was corrected by a proposal of Wolfdieter Lang. - Ralf Steiner, Sep 29 2019

The corresponding perimeters are given in A024364. - Wolfdieter Lang, Oct 06 2014

Note that the multiplicity of primitive Pythagorean triples (increasingly ordered) with perimeter P is not always 1. See A024408 for P numbers with multiplicity k >= 2, and the first example with k = 2 for P = 1716. - Wolfdieter Lang, Sep 24 2019

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 34, page 328.

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..3975
• Ron Knott, The Pythagorean triples.
• Michael Penn, Number Theory | Primitive Pythagorean Triples, Youtube video, 2019.

Crossrefs

Subsequence of A103605.

Cf. A024364, A024408.

Programs

Mathematica

A103605 = Cases[Import["https://oeis.org/A103605/b103605.txt", "Table"], {, }][[All, 2]];
SortBy[Select[Partition[A103605, 3], GCD @@ # == 1&], {#[[1]] + #[[2]] + #[[3]]&, If[EvenQ[#[[1]]], #[[1]], #[[2]]]&}] // Flatten (* Jean-François Alcover, May 26 2020 *)

Extensions

Corrected at the suggestion of Ralf Steiner by Wolfdieter Lang, Sep 24 2019

Errors in b-file noticed by Kevin Ryde corrected by Jean-François Alcover, May 26 2020