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

[M. F. Hasler]

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.
> >
>