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A055594
Shortest side of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.
8
3, 5, 5, 6, 10, 5, 10, 9, 4, 13, 10, 9, 8, 16, 15, 11, 7, 12, 10, 13, 13, 15, 20, 12, 15, 7, 14, 10, 3, 17, 20, 17, 20, 6, 17, 18, 11, 25, 8, 26, 5, 20, 18, 16, 32, 21, 8, 15, 25, 30, 19, 15, 13, 12, 24, 16, 17, 25, 10, 15, 30, 25, 22, 29, 14, 24, 13, 25, 15, 9, 17, 18, 29, 20, 35
OFFSET
1,1
LINKS
MATHEMATICA
max = 42; 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]]; A055594 = Sort[triangles, #1[[3]]*max^2 + #1[[2]]*max + #1[[1]] < #2[[3]]* max^2 + #2[[2]]*max + #2[[1]] &][[All, 1]](* Jean-François Alcover, Jun 12 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, May 26 2000
STATUS
approved