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

[Neil Sloane]

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.
> > >
> >
>
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