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A055593
Second longest side of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.
8
4, 5, 5, 8, 10, 12, 13, 12, 13, 14, 10, 10, 15, 17, 15, 13, 15, 16, 17, 20, 13, 15, 20, 17, 20, 24, 25, 24, 25, 25, 26, 25, 21, 25, 17, 24, 25, 25, 26, 28, 29, 20, 20, 30, 34, 28, 29, 34, 29, 30, 20, 26, 30, 35, 37, 25, 28, 34, 35, 36, 39, 25, 26, 29, 30, 32, 37, 39, 28, 40
OFFSET
1,1
LINKS
MATHEMATICA
max = 41; triangles = Reap[Do[s = (a+b+c)/2; area = Sqrt[s*(s-a)*(s-b)*(s-c)]; If[IntegerQ[area] && area > 0, Sow[{a, b, c, area}]], {a, 1, max}, {b, a, max}, {c, b, max}]][[2, 1]]; A055593 = Sort[triangles, #1[[3]]*max^2 + #1[[2]]*max + #1[[1]] < #2[[3]]* max^2 + #2[[2]]*max + #2[[1]] &][[All, 2]](* Jean-François Alcover, Jun 12 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, May 26 2000
STATUS
approved