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%I #11 Feb 16 2014 17:19:52
%S 3,6,5,9,4,13,9,8,11,7,12,10,13,12,15,7,10,3,17,17,20,6,18,11,8,26,5,
%T 18,16,21,8,15,25,19,15,13,12,16,17,25,10,15,22,14,24,13,25,15,9,17,
%U 20,26,15,17,27,12,13,39,29,24,30,21,39,14,27,26,20,25,13,24,27,25,37
%N Smallest side a of scalene integer Heronian triangles sorted by increasing c and b.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle.</a>
%t sideMax = 60; r[c_] := Reap[Do[ p = (a + b + c)/2; red = Reduce[ area > 1 && a < b < c && area^2 == p*(p - a)*(p - b)*(p - c), area, Integers]; If[red =!= False, sol = {a, b, c, area} /. {ToRules[red]}; Sow[sol]], {b, 1, c - 1}, {a, c - b, b - 1}]]; triangles = Flatten[ Reap[ Do[rc = r[c]; If[rc[[2]] =!= {}, Sow[rc[[2, 1]]]], {c, 5, sideMax}]][[2, 1]] , 2]; Sort[ triangles, Which[#1[[3]] < #2[[3]], True, #1[[3]] > #2[[3]], False, #1[[2]] < #2[[2]], True, #1[[2]] > #2[[2]], False, #1[[1]] <= #2[[1]], True, True, False] &][[All, 1]] (* _Jean-François Alcover_, Oct 29 2012 *)
%Y Cf. A046129, A046130, A046131.
%K nonn
%O 0,1
%A _Eric W. Weisstein_