Possible values of "Dropping time" A102419.

[zak seidov]

As usually..., 

The sequence (and formula?) is known:

%I A122437
%S A122437
1,3,6,8,11,13,16,19,21,24,26,29,32,34,37,39,42,44,47,50,52,55,57,60,63,
%T A122437
65,68,70,73,75,78,81,83,86,88,91,94,96,99,101,104,106,109,112,114,117,
%U A122437
119,122,125,127,130,132,135,138,140,143,145,148,150,153,156,158,161
%N A122437 Allowable values of the "dropping time" of
the Collatz (3x+1) iteration.
%C A122437 Only these numbers appear in A060445, which
tabulates the "dropping time" of odd 
               numbers. Note that all even numbers
have a "dropping time" of 1.
%F A122437 a(1)=1, a(n+1)=a(n)+A022921(n-1)+1
%F A122437 a(n+1)=floor(1+n+n*log(3)/log(2)) - T. D.
Noe (noe(AT)sspectra.com), Sep 08 2006
%t A122437 Floor[1+Range[0,100]*(1+Log[2,3])] - T. D.
Noe (noe(AT)sspectra.com), Sep 08 2006
%Y A122437 Cf. A022921 (number of 2^m between 3^n and
3^(n+1)), A122442 (least k having dropping 
               time a(n)).
%Y A122437 Adjacent sequences: A122434 A122435 A122436
this_sequence A122438 A122439 A122440
%K A122437 nice,nonn,new
%O A122437 1,2
%A A122437 T. D. Noe (noe(AT)sspectra.com), Sep 06
2006


--- David Wilson <davidwwilson at comcast.net> wrote:

> I think that with the proper definition, 1 does not
> belong in this sequence. 
> I highly suspect that when 1 is removed, most of the
> remaining values will 
> be numbers of the form ceil((log(6)/log(2)) k) for
> integer k.
> 
> ----- Original Message ----- 
> From: "zak seidov" <zakseidov at yahoo.com>
> To: <seqfan at ext.jussieu.fr>
> Sent: Saturday, September 16, 2006 6:53 AM
> Subject: Re: Possible values of "Dropping time"
> A102419.
> 
> 
> > Dear seqfans,
> >
> > Distribution of frequences of
> > "Dropping time" (DT) values
> > is remarkably similar in each 10000 n's:
> >
> > f1...f4 = frequences of DT in 1st...4th 10000 n's
> >
> > {DT,f1,f2,f3,f4}
> > {{0,1,0,0,0},
> > {1,5000,5000,5000,5000},<skip>
> > {220,0,0,0,1}}
> >
> > I guess that some (first) values
> > can be found analytically.
> >
> > Thanks, Zak
> >
> > --- zak seidov <zakseidov at yahoo.com> wrote:
> >
> >> Dear seqfans,
> >>
> >> Not yet submitted:
> >>
> >>
> >
>
0,1,3,6,8,11,13,16,19,21,24,26,29,32,34,37,39,42,44,47,50,52,55,57,60,63,65,68,70,73,75,78,81,83,86,88,91,94,96,99,101,104,106,109,112,114,117,119,122,125,127,130,132,135,150,171,205,220
> >>
> >> Possible values of  "Dropping time" A102419.
> >>
> >> Checked for n up to 40000.
> >>
> >> Can anyone check/extend entries,
> >>
> >> Thanks, Zak.
> >>

> > 
> 
> 


__________________________________________________
Do You Yahoo!?
Tired of spam?  Yahoo! Mail has the best spam protection around 
http://mail.yahoo.com