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

[David Seal]

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/