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

1,2

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)

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

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 *)

Crossrefs

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

Sequence in context: A108987 A035405 A280867 * A063622 A162152 A280252

Adjacent sequences: A111055 A111056 A111057 * A111059 A111060 A111061

Keyword

easy,nonn,changed

Author

Jonathan Vos Post, Oct 07 2005

Status

approved