A070115 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an isosceles integer triangle.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 18, 19, 22, 23, 24, 26, 27, 28, 31, 32, 34, 35, 38, 39, 40, 43, 46, 47, 48, 51, 52, 54, 55, 58, 61, 63, 64, 65, 68, 71, 72, 73, 76, 81, 82, 84, 85, 88, 91, 93, 94, 95, 98, 103, 104, 107, 108

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Examples

			26 is a term because [A070080(26), A070081(26), A070082(26)] = [4=4<6].
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..365
• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

Cf. A059169, A070116, A070117, A070124, A070125, A070126, A070133, A070134, A070135.

Programs

Mathematica

m = 55 (* max perimeter *);
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
Position[triangles, {a_, a_, b_} | {a_, b_, b_}] // Flatten (* Jean-François Alcover, Oct 12 2021 *)