

A046128


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


5



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
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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]] (* JeanFrançois 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



