A108229 n occurs Lucas number L(n) times (A000204).

1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8

Offset

1,2

Comments

This is the Lucas number equivalent of "n occurs A000045(n) times" (A072649), which is one of an infinite number of sequences derived from the Self-Counting Sequence [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (A002024)] which consists of 1 copy of 1, 2 copies of 2, 3 copies of 3 and so on. These include Golomb's sequence, also known as Silverman's sequence (A001462) and the like. As with these others, the challenge is to give a surprisingly simple closed-form formula for a(n).

Links

Table of n, a(n) for n=1..74.

Formula

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(3*sqrt(3)) (A073010). - Amiram Eldar, Feb 18 2024

Example

Because the first few Lucas numbers L(n), for n = 1, 2, 3, ... are 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, the current sequence consists of 1 one, 3 twos, 4 threes, 7 fours, 11 fives, 29 sixes, 47 sevens, 76 eights, 123 nines and so on.

Mathematica

Flatten[Table[Table[n, {LucasL[n]}], {n, 8}]] (* Harvey P. Dale, Feb 04 2015 *)

Crossrefs

Cf. A000204, A002024, A001462, A072649, A073010.

Sequence in context: A331255 A362881 A317359 * A023966 A368942 A088141

Adjacent sequences: A108226 A108227 A108228 * A108230 A108231 A108232

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 23 2005

Status

approved