[seqfan] Re: Franklin's A166133 - does it die?

Reinhard Zumkeller reinhard.zumkeller at gmail.com
Fri Apr 3 03:54:00 CEST 2015


I tried to enhance my b256405.txt, but I had to stop the program, because I
had the impression, that it was not only slow, but would also eat my
computer's resources. Termination during calculation of a(14036) after a
run of 1262 occurrences of 6158. Sorry . . .
Best
Reinhard



2015-04-01 22:15 GMT+02:00 Neil Sloane <njasloane at gmail.com>:

> A166133  is defined by
> After initial 1,2,4, a(n+1) is the smallest divisor of a(n)^2-1 that has
> not yet appeared in the sequence.
>
> There are a lot of huge outlying terms, but the bulk
> of the terms seem to lie on a straight line, roughly.
>
> It would die if all divisors of a(n)^2-1 were already present
>
> There is a risk of this happening if a small number M say was missing for a
> long time, but eventually appeared, long after the average term had risen
> above M^2.
>
> So we might look at the smallest missing number after n terms, A256405, and
> ask how fast it grows (see also A256408).  Reinhard Z. has produced a
> b-file of 10000 terms, but that is not enough to get a clear picture of the
> growth.
>
> It may be that A256405 also has linear growth,  in which case there
> is less chance that A166133 dies.
>
> But if A256405 grows like sqrt(n), there could be trouble.
>
> Maybe someone could extend A256405 a very long way,
> so we get a better idea of its growth rate - enough so we can estimate how
> far we would have to go to see A246505(n) around sqrt(A166133(n)) , if that
> ever happens.
>
> Alternatively, of course, find a proof that A166133 is infinite!
>
> Best regards
> Neil
>
> 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/
>



More information about the SeqFan mailing list