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

5, 10, 13, 15, 15, 15, 17, 17, 20, 20, 20, 21, 21, 25, 25, 25, 26, 26, 26, 28, 29, 29, 30, 30, 30, 30, 30, 34, 34, 35, 35, 35, 36, 37, 37, 37, 37, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 41, 41, 41, 42, 42, 44, 44, 45, 45, 45, 45, 48, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51

Offset

0,1

Links

Table of n, a(n) for n=0..68.

Eric Weisstein's World of Mathematics, Heronian Triangle.

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

Crossrefs

Cf. A046128, A046129, A046131.

Sequence in context: A242307 A313377 A224448 * A241143 A073503 A313378

Adjacent sequences: A046127 A046128 A046129 * A046131 A046132 A046133

Keyword

nonn

Author

Eric W. Weisstein

Status

approved