A119795: two graphs

[Mitch Harris]

> From: franktaw at netscape.net [mailto:franktaw at netscape.net] 
> Sent: Monday, August 07, 2006 10:28 AM
...
> Question: what is the asymptotic behavior of this sequence?  Up to 
> 1000, it looks like it might be approaching linearity, approximately 
> 7n.  However, up to 212, it looks like a slope of about 5/2; so it 
> wouldn't surprise me if it takes some other trajectory at some point.

By looking at bigger and bigger pictures, it looks like:

  - it has a divide and conquer recurrence of order 6
      a(n) = some function of a(floor((n/6))

  - a(6^n - 3) = 2*2^(4n) (but inbetween the values are above and below 
the asymptotic line)

Mitch

> If we assume that values are randomly distributed between 0 and a(n), 
> we get (leaving out various constants) the differential 
> equation dy/dx 
> = log y, or x = li(y).  From this, we get approximately a(n) 
> = n log n. 
>   In fact, n log n is not a bad match, considering the 
> irregular jumps 
> in the sequence.  1/2 n (log n) (log log n) may be a better match.
> 
> Franklin T. Adams-Watters
> 
> 
> -----Original Message-----
> From: zak seidov <zakseidov at yahoo.com>
> 
> Two graphs of this (interesting) SEQ,
> thanks, Zak
> 
> Is it (attaching files) against this list policy?
> 
> %S A119795
> 1,1,2,3,3,4,7,5,8,13,9,14,11,15,12,19,13,20,17,21
> %N A119795 a(1)=a(2)=1. a(n)=a(n-2)+(largest power of
> 2 dividing a(n-1)).
> %A A119795 Leroy Quet
> 
>