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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

%I #50 May 26 2020 15:50:02

%S 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 60,61,16,63,65,33,56,65,48,55,73,13,84,85,36,77,85,39,80,89,20,99,

%U 101,65,72,97

%N 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 The NAME was corrected by a proposal of _Wolfdieter Lang_. - _Ralf Steiner_, Sep 29 2019

%C The corresponding perimeters are given in A024364. - _Wolfdieter Lang_, Oct 06 2014

%C 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

%H Jean-François Alcover, <a href="/A103606/b103606.txt">Table of n, a(n) for n = 1..3975</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">The Pythagorean triples</a>.

%H Michael Penn, <a href="https://www.youtube.com/watch?v=F3dR41ItmSg">Number Theory | Primitive Pythagorean Triples</a>, Youtube video, 2019.

%t A103605 = Cases[Import["https://oeis.org/A103605/b103605.txt", "Table"], {_, _}][[All, 2]];

%t SortBy[Select[Partition[A103605, 3], GCD @@ # == 1&], {#[[1]] + #[[2]] + #[[3]]&, If[EvenQ[#[[1]]], #[[1]], #[[2]]]&}] // Flatten (* _Jean-François Alcover_, May 26 2020 *)

%Y Subsequence of A103605.

%Y Cf. A024364, A024408.

%K easy,nonn,tabf

%O 1,1

%A _Alexandre Wajnberg_, Mar 24 2005

%E Corrected at the suggestion of _Ralf Steiner_ by _Wolfdieter Lang_, Sep 24 2019

%E Errors in b-file noticed by _Kevin Ryde_ corrected by _Jean-François Alcover_, May 26 2020

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)