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

[Éric Angelini]

Thanks David! I hope someone will
find more and longer loops! But perhaps did you terminate the subject!
Best,
É.

> Le 1 nov. 2019 à 10:50, David Seal <david.j.seal at gwynmop.com> a écrit :
> 
> 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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