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<TITLE>Perimeters of Pythagorean Triangles</TITLE>
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<P><FONT FACE="Courier">SeqFans,</FONT>
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<P><FONT FACE="Courier">I just submitted:</FONT>
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<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>
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<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>
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<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>
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<P><FONT FACE="Courier">Publication Data:<B></B> </FONT><A HREF="http://store.yahoo.com/doverpublications/0486432785.html"><U><FONT COLOR="#0000FF" FACE="Courier">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 COLOR="#0000FF" FACE="Courier">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>
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<P><FONT FACE="Courier">Thanks</FONT>
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<P><FONT FACE="Courier">Hugo</FONT>
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