A119795: two graphs

[franktaw at netscape.net]

Continuing up to 1000, the behavior is similar, with a few double 
jumps.  Starting at 212, we have:

511,512,1023,513,1024,1537,1025,...

at 426, the sequence is:

1534,2047,1535,2048,3583,2049,3584,2561,3585,2562,...

and at 860, it goes:

5631,4608,6143,4609,6144,6657,6145,6658,...

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.

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