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Odd legs of primitive Pythagorean triples (with multiplicity) sorted with respect to increasing hypotenuse.
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%I #34 Jun 19 2022 23:23:14

%S 3,5,15,7,21,35,9,45,11,63,33,55,77,13,39,65,99,91,15,117,105,143,17,

%T 51,85,119,165,19,153,57,95,195,187,133,171,21,221,105,209,255,247,23,

%U 69,115,231,161,285,273,207,25,75,323,253,175,299,225,357,27,275,345,135,189,325

%N Odd legs of primitive Pythagorean triples (with multiplicity) sorted with respect to increasing hypotenuse.

%C The primary key is the increasing length of the hypotenuse, A020882. If there is more than one solution with that hypotenuse, the (secondary) sorting key is the even leg.

%C Only the odd legs 'a' of reduced triangles with gcd(a,b,c)=1, a^2+b^2=c^2, a=q^2-p^2, b=2*p*q, c=q^2+p^2, gcd(p,q)=1 are listed.

%H K. G. Stier, <a href="/A180620/b180620.txt">Table of n, a(n) for n = 1..1593</a>

%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/rtritab.txt"> Pythagorean Triple Table, Reduced integer right triangles</a>, Feb 28, 1998.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean Triple</a>.

%H <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>.

%e a(1) = 3 because the only triangle with the least possible hypotenuse 5 has catheti 3 and 4.

%Y Cf. A046086, A046087, A020882, A081874, A231100.

%K nonn,look

%O 1,1

%A _Jonathan Vos Post_, Sep 12 2010

%E Comment on sorting added, more terms appended by _R. J. Mathar_, Oct 15 2010

%E Sequence's name and comments corrected by _K. G. Stier_, Nov 03 2013