[seqfan] Re: number 999999000000

[Max Alekseyev]

Hi Neil,

It started from a question in Russian forum dxdy.ru about the
(in)finiteness of what is now A261205 from Yan Denenberg (a co-author of
A261205). This question ringed a bell in my head about A006446, which I
happened to analyze before. To my surprise, the corresponding sequence
(A261205) was not in the OEIS and I proceeded with adding it and other
sister sequences (A261206, A261341, A261342). Most amazing thing was the
discovery that 999999000000 is an element of A261206 and apparently the
largest one (I believe this sequence is finite).

It is possible to generalize this class of sequences by taking some
integer-valued function f(n,k) decreasing in k such that f(n,1)=n and
f(n,m)=c (say, c=1 or c=2) for all large enough m and considering those n
that are divisible by all f(n,1), f(n,2), ... If f(n,k) is slowly
decreasing in k, then the set corresponding n's is likely have very small
number (if any) of terms, while if f(n,k) decreases rapidly, then there
will be too many suitable n's. I believe the balance is achieved at
functions like f(n,k) = floor(n^(1/k)) so that f(n,k) stabilizes to c at k
~= log(n).

Regards,
Max


On Sat, Aug 15, 2015 at 11:28 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Max, these are very interesting sequences!
>
> Could you say why you invented A261205 and A261206 in the first place? What
> was the background?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sat, Aug 15, 2015 at 11:01 AM, Max Alekseyev <maxale at gmail.com> wrote:
>
> > Giovanni -- thanks for the update on the lower bound.
> >
> > I've added two new sequences of the same flavor:
> >
> > http://oeis.org/A261341
> > http://oeis.org/A261342
> >
> > where the latter is a supersequence (i.e. contains all other as
> > subsequences) and has the best chances for being infinite. I was able to
> > determine 278 terms below 10^16 in it, with the largest one being
> > 8947091986560.
> >
> > Extensions and improved lower bounds are welcome.
> >
> > Regards,
> > Max
> >
> >
> >
> >
> >
> > On Thu, Aug 13, 2015 at 3:33 PM, Giovanni Resta <g.resta at iit.cnr.it>
> > wrote:
> >
> > > On 08/13/2015 05:54 PM, Max Alekseyev wrote:
> > >
> > > Same question applies to the sister sequence  http://oeis.org/A261205
> > >>
> > >
> > > Nice sequences. For the sister sequence A261205 I searched further
> terms,
> > > without success, up to 10^23.
> > >
> > > Giovanni
> > >
> > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>