1 2 1 3 1 2 1 4 1 2 1 ...

[Edwin Clark]

n Mon, 26 Apr 2004, Henry Gould wrote:

> Can anyone interpret the sequece below?
> 
> 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2
> 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 7 1 2 1 3 1 2 1 4 1 2 1 3
> 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2
> 1 3 1 2 1 4 1 2 1 3 1 2 1 8 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4
> 1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2
> 1 7 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3
> 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
> . . . . .
> 

After removing the 1's it appears to match:

ID Number: A085058
URL:       http://www.research.att.com/projects/OEIS?Anum=A085058
Sequence:  2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,
           2,7,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,
           2,3,2,8,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,
           2,4,2,3,2,7,2,3,2,4,2,3,2,5,2
Name:      Number of steps for iteration of map x -> (3/2)*ceiling(x) to 
reach
              an integer when started at 2*n+1.
Comments:  Also number of steps for iteration of map x -> (3/2)*floor(x) 
to
              reach an integer when started at 2*n+3. - Benoit Cloitre, 
Sep 27 2003
           The first time that a(n) = e+1 is when n is of the form 2^e - 
1. - RGWv Sep 28
              2003. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 29 2003
           Add 1 to each term of A001511 to get A085058. - Gary W. Adamson
              (qntmpkt(AT)yahoo.com), Sep 29 2003