# A sequence related to Lionel Levile's sequence?

Alexandre Wajnberg alexandre.wajnberg at skynet.be
Fri Nov 4 16:54:30 CET 2005

```Looks like Golomb's sequence A001462:

ID Number: A001462 (Formerly M0257 and N0091)
URL:       http://www.research.att.com/projects/OEIS?Anum=A001462
Sequence:  1,2,2,3,3,4,4,4,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,9,10,
10,10,10,10,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,
13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,
17,17,17,17,17,17,17,18,18,18,18,18,18,18,19
Name:      Golomb's sequence: a(n) is the number of times n occurs, starting
with a(1) = 1.
Comments:  It is understood that a(n) is taken to be the smallest number >=
a(n-1) which is compatible with the description.
Also called Silverman's sequence.
Vardi gives several identities satisfied by A001463 and this
sequence.

Alexandre

---------------------------------------

> I just submitted the following sequence:
>
> %I A113676
> %S A113675
> 1,2,3,3,4,4,4,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,9,10,10,10,10,10,11,11,1
> 1,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15
> ,15,16,16,16,16,16,16,16,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,
> 19,19,19,19
> %N A113675 Nondecreasing sequence in which a(n) describes how many times n+1
> is in the sequence, with a(1)=1.
> %C A113675 This sequence can be divided into rows forming a triangle as
> follows: start with a(1)=1 as the first row. The row sum of row n-1 gives
> the number of elements in row n. This triangle starts 1; 2; 3,3;
> 4,4,4,5,5,5; ...
> The final elements of this row seem to form Lionel Levile's sequence
> A014644, except that 2 isn't duplicate.
> %e A113675 a(9)=5 so 10 appears five times in the sequence.
> %O A113675 1
> %K A113675 nonn,easy
> %A A113675 Floor van Lamoen (fvlamoen at hotmail.com), Nov 04 2005
>
> I cannot fully understand if indeed we find Lionel Levile's sequence as
> described. Perhaps I am missing something.
>
> Kind regards,
> Floor.
>
>

```