

A108229


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


0



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
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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 SelfCounting 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 closedform formula for a(n).


LINKS

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


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.
Sequence in context: A089051 A331255 A317359 * A023966 A088141 A185283
Adjacent sequences: A108226 A108227 A108228 * A108230 A108231 A108232


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jul 23 2005


STATUS

approved



