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A055593 Second longest side of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.

%I A055593 #8 Jul 30 2017 15:37:15
%S A055593 4,5,5,8,10,12,13,12,13,14,10,10,15,17,15,13,15,16,17,20,13,15,20,17,
%T A055593 20,24,25,24,25,25,26,25,21,25,17,24,25,25,26,28,29,20,20,30,34,28,29,
%U A055593 34,29,30,20,26,30,35,37,25,28,34,35,36,39,25,26,29,30,32,37,39,28,40
%N A055593 Second longest side of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.
%H A055593 Ray Chandler, <a href="/A055593/b055593.txt">Table of n, a(n) for n = 1..10000</a>
%t A055593 max = 41; triangles = Reap[Do[s = (a+b+c)/2; area = Sqrt[s*(s-a)*(s-b)*(s-c)]; If[IntegerQ[area] && area > 0, Sow[{a, b, c, area}]], {a, 1, max}, {b, a, max}, {c, b, max}]][[2, 1]]; A055593 = Sort[triangles, #1[[3]]*max^2 + #1[[2]]*max + #1[[1]] < #2[[3]]* max^2 + #2[[2]]*max + #2[[1]] &][[All, 2]](* _Jean-François Alcover_, Jun 12 2012 *)
%Y A055593 Cf. A055592, A055594, A055595.
%K A055593 nonn
%O A055593 1,1
%A A055593 _Henry Bottomley_, May 26 2000