A046128 Smallest side a of scalene integer Heronian triangles sorted by increasing c and b.

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, 18, 16, 21, 8, 15, 25, 19, 15, 13, 12, 16, 17, 25, 10, 15, 22, 14, 24, 13, 25, 15, 9, 17, 20, 26, 15, 17, 27, 12, 13, 39, 29, 24, 30, 21, 39, 14, 27, 26, 20, 25, 13, 24, 27, 25, 37

Offset

0,1

Links

Table of n, a(n) for n=0..72.

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

Crossrefs

Cf. A046129, A046130, A046131.

Sequence in context: A059770 A019690 A010620 * A342222 A331164 A057098

Adjacent sequences: A046125 A046126 A046127 * A046129 A046130 A046131

Keyword

nonn

Author

Eric W. Weisstein

Status

approved