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A046130 Largest side c of a scalene integer Heronian triangles sorted by increasing c and b. 5

%I

%S 5,10,13,15,15,15,17,17,20,20,20,21,21,25,25,25,26,26,26,28,29,29,30,

%T 30,30,30,30,34,34,35,35,35,36,37,37,37,37,39,39,39,39,39,40,40,40,40,

%U 40,41,41,41,42,42,44,44,45,45,45,45,48,50,50,50,50,50,51,51,51,51,51

%N Largest side c of a 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, 3]] (* _Jean-Fran├žois Alcover_, Oct 29 2012 *)

%Y Cf. A046128, A046129, A046131.

%K nonn

%O 0,1

%A _Eric W. Weisstein_

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)