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

[Alex M]

A question worth asking would be, for a certain base k that we do this
process in, are there some integers p and q st. a(n)=p*k^(n-q) for
sufficiently large n? For k=10, p=1008 and q=2, for instance. Sort of
extracting non-base-y part of the idea, that such a sequence [may or may
not] exist. :P

Very cool fact that does in our home of decimal! :D

~6 out of 5 statisticians say that the
number of statistics that either make
no sense or use ridiculous timescales
at all has dropped over 164% in the
last 5.62474396842 years.


On Sat, Jan 18, 2014 at 9:52 AM, Alonso Del Arte
<alonso.delarte at gmail.com>wrote:

> 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/
> >
>
>
>
> --
> Alonso del Arte
> Author at SmashWords.com<
> https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
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