A046129 Middle side b of scalene integer Heronian triangles sorted by increasing c and b.

4, 8, 12, 12, 13, 14, 10, 15, 13, 15, 16, 17, 20, 17, 20, 24, 24, 25, 25, 25, 21, 25, 24, 25, 26, 28, 29, 20, 30, 28, 29, 34, 29, 20, 26, 30, 35, 25, 28, 34, 35, 36, 26, 30, 32, 37, 39, 28, 40, 40, 34, 40, 37, 39, 36, 39, 40, 42, 35, 34, 40, 41, 41, 48, 30, 35, 37, 38, 40

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Heronian Triangle.

Crossrefs

Cf. A046128, A046130, A046131.

Programs

Mathematica

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, 2]] (* Jean-François Alcover, Oct 29 2012 *)