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%I #21 Nov 14 2019 21:22:24
%S 4,12,8,24,20,12,40,28,60,16,56,48,36,84,80,72,20,60,112,44,88,24,144,
%T 140,132,120,52,180,104,176,168,28,84,156,140,220,60,208,120,32,96,
%U 264,260,252,160,240,68,136,224,312,308,36,204,288,180,272,76,364,252,152,352,340,228
%N Even 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 (increasing) even leg - that is, the terms go in the increasing order. [Corrected by _Andrey Zabolotskiy_, Oct 31 2019]
%C Only the even legs 'b' 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="/A231100/b231100.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>.
%F a(n) = sqrt(A020882(n)^2-A180620(n)^2).
%e a(13) = sqrt(A020882(13)^2-A180620(13)^2) = sqrt(85^2-77^2) = sqrt(1296) = 36.
%Y Cf. A020882, A180620.
%K nonn,look
%O 1,1
%A _K. G. Stier_, Nov 03 2013
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