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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.

%I A103606 #53 Jan 03 2025 11:48:21
%S A103606 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,
%T A103606 60,61,16,63,65,33,56,65,48,55,73,13,84,85,36,77,85,39,80,89,20,99,
%U A103606 101,65,72,97
%N 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.
%C A103606 The NAME was corrected by a proposal of _Wolfdieter Lang_. - _Ralf Steiner_, Sep 29 2019
%C A103606 The corresponding perimeters are given in A024364. - _Wolfdieter Lang_, Oct 06 2014
%C A103606 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
%D A103606 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 34, page 328.
%H A103606 Jean-François Alcover, <a href="/A103606/b103606.txt">Table of n, a(n) for n = 1..3975</a>
%H A103606 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">The Pythagorean triples</a>.
%H A103606 Michael Penn, <a href="https://www.youtube.com/watch?v=F3dR41ItmSg">Number Theory | Primitive Pythagorean Triples</a>, Youtube video, 2019.
%t A103606 A103605 = Cases[Import["https://oeis.org/A103605/b103605.txt", "Table"], {_, _}][[All, 2]];
%t A103606 SortBy[Select[Partition[A103605, 3], GCD @@ # == 1&], {#[[1]] + #[[2]] + #[[3]]&, If[EvenQ[#[[1]]], #[[1]], #[[2]]]&}] // Flatten (* _Jean-François Alcover_, May 26 2020 *)
%Y A103606 Subsequence of A103605.
%Y A103606 Cf. A024364, A024408.
%K A103606 easy,nonn,tabf
%O A103606 1,1
%A A103606 _Alexandre Wajnberg_, Mar 24 2005
%E A103606 Corrected at the suggestion of _Ralf Steiner_ by _Wolfdieter Lang_, Sep 24 2019
%E A103606 Errors in b-file noticed by _Kevin Ryde_ corrected by _Jean-François Alcover_, May 26 2020