[seqfan] Re: Add (to me) my even biggest digit

[M. F. Hasler]

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