[seqfan] Re: As much as I hate "base" sequences...

[Neil Sloane]

David, That IS a nice sequence.
Please submit it, giving as many terms as you can
prove are correct. (And of course state your conjecture about
the general term)
Neil


On Fri, Jan 17, 2014 at 7:26 PM, David Wilson <davidwwilson at comcast.net>wrote:

> Start with k and repeatedly apply the function
>
> k -> k / sum of digits of k
>
> stopping when there is a positive remainder or the divisor is 1.
>
> The smallest survivors of n iterations among the 29-smooth numbers are
>
> 0 1
> 1 2
> 2 12
> 3 108
> 4 1944
> 5 52488
> 6 1102248
> 7 44641044
> 8 1008000000
> 9 10080000000
> 10 100800000000
> 11 1008000000000
> 12 10080000000000
> 13 100800000000000
> 14 1008000000000000
> 15 10080000000000000
> 16 100800000000000000
> 17 1008000000000000000
> 18 10080000000000000000
>
> I am all but certain that these are these are indeed the smallest survivors
> among the integers, and that the sequence extends to infinity in the
> obvious
> way.
>
> The change in behavior at a(8) surprised me at first. a(1) through a(7)
> eventually reach 1.  For n >= 8, we have
>
> a(n) = 1008*10^(n-2) ->  112*10^(n-2) -> 28*10^(n-2) -> 28*10^(n-3) -> ...
> -> 28.
>
> ending at 28 after n iterations.
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com