[seqfan] Re: A242927

Neil Sloane njasloane at gmail.com
Sat Mar 24 12:59:02 CET 2018


After adding 1806 to A242927, it becomes the same as the "fini,full"
sequence A014117,
which is defined by
Numbers n such that m^(n+1) == m (mod n) holds for all m.
Is this a coincidence, a conjecture, a theorem?
Don said A242927 has no further terms - is that a theorem?
Should the two entries now be merged?

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


On Fri, Mar 23, 2018 at 10:46 PM, Sean A. Irvine <sairvin at gmail.com> wrote:

> Yes, such a number is well within reach of standard elliptic curve
> primality proving software such as Primo .  However, it is still a fairly
> lengthy computation, it would likely take days to complete (at least with
> my resources).
>
> See: http://www.ellipsa.eu/public/primo/top20.html
>
> On 24 March 2018 at 14:36, Don Reble <djr at nk.ca> wrote:
>
> > Seqfans:
> >
> > %I A242927
> >> %S 1,2,6,42
> >> %N Numbers n such that k^n + (k+1)^n + ... + (k+n-1)^n is prime for some
> >> k.
> >>
> >
> >    There's only one more term of A242927: a(5)=1806. A resulting
> >    "prime" (k=3081) has 6663 digits: so far it's just a rather strong
> >    (Miller-Rabin) probable prime.
> >    Is it possible to prove primality for such a big number?
> >
> > --
> > Don Reble  djr at nk.ca
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>


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