Perimeters of Pythagorean Triangles

[David Wilson]

Perimeters of Pythagorean TrianglesExtensions:

%S A099829 12,60,120,240,420,720,840,840,1680,1680,2520,2520,4620,5040,5040,5040,9240,
%T A099829 9240,9240,9240,18480,18480,18480,18480,18480,27720,27720,27720,27720,27720,
%U A099829 27720,55440,55440,55440,55440,55440,55440,55440,55440,55440,110880,110880

%S A099830 12,60,120,240,420,720,1320,840,2640,1680,3360,2520,4620,7920,7560,5040,
%T A099830 10080,17160,10920,9240,40320,25200,28560,21840,18480,60480,41580,46200,
%U A099830 36960,32760,27720,78540,60060,129360,134640,115920,85680,65520,83160
  ----- Original Message ----- 
  From: Pfoertner, Hugo 
  To: 'seqfan at ext.jussieu.fr' 
  Sent: Wednesday, October 27, 2004 9:11 AM
  Subject: Perimeters of Pythagorean Triangles


  SeqFans, 

  I just submitted: 

  %S A099829 12 60 120 240 420 720 840 840 1680 1680 2520 2520 4620 
  %N A099829 Smallest perimeter S such that at least n distinct Pythagorean triangles with this perimeter can be constructed.

  %H A099829 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>

  %H A099829 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ps.html">Index entries related to Pythagorean Triples.</a>

  %e A099829 a(3)=120 because 120 is the smallest possible perimeter for which 3 different Pythgorean triangles exist: 120=20+48+52=24+45+51=30+40+50.

  %Y A099829 Cf. A099830 first perimeter with exact match of number of Pythagorean triangles, A009096 ordered perimeters of pythagorean triangles.

  %O A099829 1 
  %K A099829 ,more,nonn, 
  %A A099829 Hugo Pfoertner (hugo at pfoertner.org), Oct 27 2004 

  %I A099830 %S A099830 12 60 120 240 420 720 1320 840 2640 1680 3360 2520 4620 
  %N A099830 Smallest perimeter S such that exactly n distinct Pythagorean triangles with this perimeter can be constructed. %e A099830 a(7)=1320 because 1320 is the smallest possible perimeter for which exactly 7 different Pythgorean triangles exist: 1320 = 110+600+610 = 120+594+606 = 220+528+572 = 231+520+569 = 264+495+561 = 330+440+550 = 352+420+548. 

  %Y A099830 Cf. A099829 first perimeter producing at least n Pythagorean triangles, A009096 ordered perimeters of Pythagorean triangles, A001399, A069905 partitions into 3 parts. 

  %O A099830 1 
  %K A099830 ,more,nonn, 
  %A A099830 Hugo Pfoertner (hugo at pfoertner.org), Oct 27 2004 

  Would be nice if someone can try to extend both (or add more information). Does anyone have access to the the book: 

  Publication Data: Pythagorean Triangles, by Waclaw Sierpinski. Dover Publications, 2003. Paperback, 107 pp, $9.95. ISBN 0-486-43278-5 ? From the review given in

  http://www.maa.org/reviews/pythtriangles.html 
  I suspect, that there might be related information in this book. 

  Thanks 

  Hugo 
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