<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD><TITLE>Perimeters of Pythagorean Triangles</TITLE>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.2900.2523" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2>Extensions:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>%S A099829
12,60,120,240,420,720,840,840,1680,1680,2520,2520,4620,5040,5040,5040,9240,<BR>%T
A099829
9240,9240,9240,18480,18480,18480,18480,18480,27720,27720,27720,27720,27720,<BR>%U
A099829
27720,55440,55440,55440,55440,55440,55440,55440,55440,55440,110880,110880</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>%S A099830
12,60,120,240,420,720,1320,840,2640,1680,3360,2520,4620,7920,7560,5040,<BR>%T
A099830
10080,17160,10920,9240,40320,25200,28560,21840,18480,60480,41580,46200,<BR>%U
A099830
36960,32760,27720,78540,60060,129360,134640,115920,85680,65520,83160</FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=Hugo.Pfoertner@muc.mtu.de
href="mailto:Hugo.Pfoertner@muc.mtu.de">Pfoertner, Hugo</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=seqfan@ext.jussieu.fr
href="mailto:'seqfan@ext.jussieu.fr'">'seqfan@ext.jussieu.fr'</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, October 27, 2004 9:11
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Perimeters of Pythagorean
Triangles</DIV>
<DIV><BR></DIV>
<P><FONT face=Courier>SeqFans,</FONT> </P>
<P><FONT face=Courier>I just submitted:</FONT> </P>
<P><FONT face=Courier>%S A099829 12 60 120 240 420 720 840 840 1680 1680 2520
2520 4620 </FONT><BR><FONT face=Courier>%N A099829 Smallest perimeter S such
that at least n distinct Pythagorean triangles with this perimeter can be
constructed.</FONT></P>
<P><FONT face=Courier>%H A099829 Eric Weisstein's World of Mathematics, <a
href="<A href="http://mathworld.wolfram.com/PythagoreanTriple.html"
target=_blank>http://mathworld.wolfram.com/PythagoreanTriple.html</A>">Pythagorean
Triple.</a></FONT></P>
<P><FONT face=Courier>%H A099829 <a href="<A
href="http://www.research.att.com/~njas/sequences/Sindx_Ps.html"
target=_blank>http://www.research.att.com/~njas/sequences/Sindx_Ps.html</A>">Index
entries related to Pythagorean Triples.</a></FONT></P>
<P><FONT face=Courier>%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.</FONT></P>
<P><FONT face=Courier>%Y A099829 Cf. A099830 first perimeter with exact match
of number of Pythagorean triangles, A009096 ordered perimeters of pythagorean
triangles.</FONT></P>
<P><FONT face=Courier>%O A099829 1 </FONT><BR><FONT face=Courier>%K A099829
,more,nonn,</FONT> <BR><FONT face=Courier>%A A099829 Hugo Pfoertner
(hugo@pfoertner.org), Oct 27 2004</FONT> </P>
<P><FONT face=Courier>%I A099830 %S A099830 12 60 120 240 420 720 1320 840
2640 1680 3360 2520 4620 </FONT><BR><FONT face=Courier>%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. </FONT></P>
<P><FONT face=Courier>%Y A099830 Cf. A099829 first perimeter producing at
least n Pythagorean triangles, A009096 ordered perimeters of Pythagorean
triangles, A001399, A069905 partitions into 3 parts. </FONT></P>
<P><FONT face=Courier>%O A099830 1 </FONT><BR><FONT face=Courier>%K A099830
,more,nonn,</FONT> <BR><FONT face=Courier>%A A099830 Hugo Pfoertner
(hugo@pfoertner.org), Oct 27 2004</FONT> </P>
<P><FONT face=Courier>Would be nice if someone can try to extend both (or add
more information). Does anyone have access to the the book:</FONT> </P>
<P><FONT face=Courier>Publication Data:<B></B> </FONT><A
href="http://store.yahoo.com/doverpublications/0486432785.html"><U><FONT
face=Courier color=#0000ff>Pythagorean Triangles</FONT></U></A><FONT
face=Courier>, by Waclaw Sierpinski. Dover Publications, 2003. Paperback, 107
pp, $9.95. ISBN 0-486-43278-5 ? From the review given in</FONT></P>
<P><A href="http://www.maa.org/reviews/pythtriangles.html"><U><FONT
face=Courier
color=#0000ff>http://www.maa.org/reviews/pythtriangles.html</FONT></U></A>
<BR><FONT face=Courier>I suspect, that there might be related information in
this book.</FONT> </P>
<P><FONT face=Courier>Thanks</FONT> </P>
<P><FONT face=Courier>Hugo</FONT> </P></BLOCKQUOTE></BODY></HTML>