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

[Alonso Del Arte]

Once in a blue moon a genuinely interesting base sequence comes along and
we remember they're not all based on aimless digit shuffling. The trends
seem to indicate there might come a point we get very tired of sequences "x
such that f(x) is prime" even when f(x) does not involve a particular base.


On Sat, Jan 18, 2014 at 10:49 AM, Neil Sloane <njasloane at gmail.com> wrote:

> 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
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



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Alonso del Arte
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