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.

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

Author

Henry Bottomley, May 26 2000

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055592, A055593, A055595.

Programs

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 *)