[seqfan] Re: apparently unique infinite sequences related to the sum of divisors

[Neil Sloane]

Max, You said:

I have verified that all its values below 10^10 are uniquely
defined (all possible bifurcations die sooner or later). So we can be sure
that there is no dead end for A259934.

Me: But it is possible that A259934 reaches a dead end after 10^100
steps, right?  So then we would need to backtrack and change A259934.

I don't see that any finite amount of checking will show we are on the
right track!

But I don't read Russian ....

I agree this is a very nice sequence!

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 Thu, Jul 9, 2015 at 3:22 PM, Max Alekseyev <maxale at gmail.com> wrote:

> Falcao proved that there is an infinite sequence starting with 2 (or 0 if
> you like). I have verified that all its values below 10^10 are uniquely
> defined (all possible bifurcations die sooner or later). So we can be sure
> that there is no deadend for A259934. It is an open question though if
> there exists a viable bifurcation point.
> Max
>
>
> On Thu, Jul 9, 2015 at 3:06 PM, <israel at math.ubc.ca> wrote:
>
> > How do you know your values for A259934 are correct? It's true that a(n)
> -
> > d(a(n)) = a(n-1) for the listed values, but how do you know you don't run
> > into a dead end? Falcao apparently (I don't read Russian) proved there is
> > an infinite sequence, but there are also long finite sequences that have
> > dead ends.
> >
> > Cheers,
> > Robert
> >
> >
> > On Jul 9 2015, Max Alekseyev wrote:
> >
> >  SeqFans,
> >>
> >> I'd like to draw your attention to two newly added nice sequences:
> >>
> >> http://oeis.org/A259934
> >> http://oeis.org/A259935
> >>
> >> Comments are welcome.
> >>
> >> Regards,
> >> Max
> >>
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