

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.


25



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
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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

JeanFrançois 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.


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 (* JeanFrançois Alcover, May 26 2020 *)


CROSSREFS

Subsequence of A103605.
Cf. A024364, A024408.
Sequence in context: A139369 A151555 A263728 * A139794 A202819 A185383
Adjacent sequences: A103603 A103604 A103605 * A103607 A103608 A103609


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 bfile noticed by Kevin Ryde corrected by JeanFrançois Alcover, May 26 2020


STATUS

approved



