[seqfan] Re: Add (to me) my even biggest digit
M. F. Hasler
oeis at hasler.fr
Mon Oct 13 00:33:26 CEST 2014
On Sun, Oct 12, 2014 at 5:07 PM, Neil Fernandez <primeness at borve.org> wrote:
>>Ah, thank you Juan -- I'm pretty sure now
>>that no such infinite seq is possible. At some point, it will halt.
Yes Eric, this is certain, see the proof below.
> All sequences starting with x < 100000 halt.
It is sufficient to check that all sequences starting with x < 10 halt.
Indeed, assume that there is an integer y for which the sequence never halts.
Then, since the steps are within {2,4,6,8} it will run
at one moment into an integer of the form 10^k+z with z<10
and 10^k larger than all numbers reached for starting values x<10.
>From there on it will yield the same sequence as z with all values
shifted by 10^k
and therefore stop below 2*10^k, contradiction.
--Maximilian
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