[seqfan] Re: Concatenate the sums of the neighboring digits

[M. F. Hasler]

There was some discussion on this (loops etc) on SeqFan in August 2011, cf
http://list.seqfan.eu/pipermail/seqfan/2011-August/007775.html

- Maximilian

On Fri, Nov 1, 2019, 16:27 Neil Sloane <njasloane at gmail.com> wrote:

> and the Friedman link in A053392 gives 1496 as the smallest number that
> blows up
>
> What is the sequence of numbers that blows up (or even appears to blow up)?
> 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 Fri, Nov 1, 2019 at 3:56 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > and then, as Remy Sigrist points out, it is a duplicate of A053392.
> >
> > 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 Fri, Nov 1, 2019 at 3:52 PM Neil Sloane <njasloane at gmail.com> wrote:
> >
> >> Good point, I will change it.
> >>
> >> Is 1999 the smallest number whose trajectory blows up?
> >>
> >> 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 Fri, Nov 1, 2019 at 3:43 PM M. F. Hasler <seqfan at hasler.fr> wrote:
> >>
> >>> On Fri, Nov 1, 2019, 14:19 Neil Sloane <njasloane at gmail.com> wrote:
> >>>
> >>> > I created A328556 for the one-step function.
> >>> >
> >>>
> >>> Shouldn't that function yield zero for single digit numbers?
> >>> The concatenation of sums of consecutive pairs is empty if there's no
> >>> pair.
> >>>
> >>> Maximilian
> >>>
> >>> >
> >>> > On Fri, Nov 1, 2019 at 6:41 AM David Seal <david.j.seal at gwynmop.com>
> >>> > wrote:
> >>> >
> >>> > > Another quick observation is that there are at least 9 loops other
> >>> than
> >>> > > the trivial one of the empty string of digits going to itself:
> >>> > >
> >>> > > 991 -> 1810 -> 991
> >>> > > 992 -> 1811 -> 992
> >>> > > 993 -> 1812 -> 993
> >>> > > ...
> >>> > > 999 -> 1818 -> 999
> >>> > >
> >>> > > The last of those is an exception to the "and grow" part of Hans's
> >>> > > observation, though he may have meant "strictly inside".
> >>> > >
> >>> > > Also, longer strings of 9s with a single non-zero digit at the end
> >>> are an
> >>> > > example of growing forever 'non-chaotically' - i.e. in a way that
> is
> >>> very
> >>> > > easy to predict. For instance:
> >>> > >
> >>> > > 9991 -> 181810 -> 99991 -> 18181810 -> 9999991 -> 181818181810 ->
> >>> > > 99999999991 -> ...
> >>> > >
> >>> > > has strings of 2+2^n 9s followed by a 1 growing to similar strings
> >>> with n
> >>> > > incremented by 1 every two generations.
> >>> > >
> >>> > > David
> >>> > >
> >>> > >
> >>> > > > On 01 November 2019 at 04:27 Hans Havermann <gladhobo at bell.net>
> >>> wrote:
> >>> > > >
> >>> > > >
> >>> > > > Note that whenever three or more 9s find themselves adjacent
> >>> inside a
> >>> > > number, these segments will reproduce every second generation and
> >>> grow.
> >>> > > Continuing your 5677 example:
> >>> > > >
> >>> > > > ...
> >>> > > > 786337
> >>> > > > 15149610
> >>> > > > 665131571
> >>> > > > 12116446128
> >>> > > > 3327108107310
> >>> > > > 6598189171041
> >>> > > > 11141799171088145
> >>> > > > 22558161810881816959
> >>> > > > 4710139779918169997151414
> >>> > > >
> >>> > > > The last one has three adjacent 9s so the sequence will grow
> >>> forever.
> >>> > >
> >>> >
> >>>
> >>> --
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>
>
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>