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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.
28
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
1,1
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
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..3975
Michael Penn, Number Theory | Primitive Pythagorean Triples, Youtube video, 2019.
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 *)
CROSSREFS
Subsequence of A103605.
Sequence in context: A151555 A263728 A370760 * A139794 A369493 A365796
KEYWORD
easy,nonn,tabf
AUTHOR
Alexandre Wajnberg, Mar 24 2005
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
STATUS
approved