A111058 Numbers k such that the average of the first k Lucas numbers is an integer.

1, 2, 8, 12, 20, 24, 48, 60, 68, 72, 92, 96, 120, 140, 144, 188, 192, 200, 212, 216, 240, 288, 300, 332, 336, 360, 384, 428, 432, 440, 452, 480, 500, 548, 576, 600, 648, 660, 668, 672, 680, 692, 696, 720, 768, 780, 788, 812, 864, 908, 932, 960, 1008, 1028, 1052

Offset: 1

Author

Jonathan Vos Post, Oct 07 2005

Keywords

• easy
• nonn

Comments

A111035 is the equivalent for Fibonacci numbers and has many elements in common with this sequence. T. D. Noe, who extended this sequence, noticed that, for some reason, 24 divides many of those k.

All terms are even except for the first term. - Harvey P. Dale, Apr 22 2024

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A000032, A000204, A027961, A111035, A160665.

Programs

Mathematica

Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; lst={}; s=0; Do[s=s+Lucas[n]; If[Mod[s, n]==0, AppendTo[lst, n]], {n, 1000}]; lst (* T. D. Noe *)
Module[{nn=1000,ln},ln=LucasL[Range[nn]];Table[If[IntegerQ[Mean[Take[ln,n]]],n,Nothing],{n,nn}]] (* Harvey P. Dale, Apr 22 2024 *)

Formula

k such that (Sum_{i=1..k} A000204(i))/k is an integer.

{ k : A027961(k) == 0 (mod k) }. - Alois P. Heinz, Apr 23 2024