A070118 Numbers n such that [A070080(n), A070081(n), A070082(n)] is an acute integer triangle.

1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 15, 16, 18, 19, 22, 23, 24, 27, 28, 31, 33, 34, 35, 38, 39, 40, 43, 45, 46, 47, 48, 51, 53, 54, 55, 58, 60, 63, 64, 65, 68, 70, 71, 72, 73, 76, 81, 83, 84, 85, 88, 90, 92, 93, 94, 95, 98, 103, 106, 107, 108

Offset

1,2

Links

Jean-François Alcover, Table of n, a(n) for n = 1..431

Reinhard Zumkeller, Integer-sided triangles

Example

a(21)=33: [A070080(33), A070081(33), A070082(33)]=[4,5,6], A070085(33)=4^2+5^2-6^2=16+25-36=5>0.

Mathematica

m = 50; (* 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_, b_, c_} /; a^2 + b^2 - c^2 > 0] // Flatten (* Jean-François Alcover, Oct 04 2021 *)

Crossrefs

Cf. A070093, A070119, A070120, A070121, A070122, A070123, A070124, A070125, A070126.

Sequence in context: A227194 A039054 A047519 * A070124 A059097 A047301

Adjacent sequences: A070115 A070116 A070117 * A070119 A070120 A070121

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved