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A046129 Middle side b of a scalene integer Heronian triangles sorted by increasing c and b. 4
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 (list; graph; refs; listen; history; text; internal format)
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, 2]] (* Jean-Fran├žois Alcover, Oct 29 2012 *)

CROSSREFS

Cf. A046128, A046130, A046131.

Sequence in context: A158457 A072905 A086481 * A092930 A009012 A046084

Adjacent sequences:  A046126 A046127 A046128 * A046130 A046131 A046132

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified November 28 07:52 EST 2014. Contains 250285 sequences.