[seqfan] Re: "Giuga-Wilson" conjecture and pseudoprimes

[Tomasz Ordowski]

Dear Maximilian,

My message was sent to the SeqFan list with great delay,
and in the meantime there has been significant progress in our research.

The sequence https://oeis.org/A308963
has been carefully checked and corrected by Max Alekseyev:

Hi Tomasz,

Now it's already a(7) there.
I've just used the definition with Bernoulli numbers (and no factorial) and
their p-adic continuity:
https://en.wikipedia.org/wiki/Bernoulli_number#p-adic_continuity

Regards,

Max A. Alekseyev
Associate Professor
George Washington University
Department of Mathematics &
Computational Biology Institute
45085 University Dr. #305
Ashburn, VA 20147
http://home.gwu.edu/~maxal
+1-571-5530259

Best regards,

Thomas

pon., 22 lip 2019 o 13:16 M. F. Hasler <oeis at hasler.fr> napisał(a):

> On Thu, Jul 18, 2019 at 12:12 PM Tomasz Ordowski <tomaszordowski at gmail.com
> >
> wrote:
>
> > P.S. Note:
> > The "Giuga-Wilson" pseudoprimes p = 77, 161, 2261, 12839, 14231, ...
> >
>
> Is this A308963 <https://oeis.org/A308963>, which has the name "Lerch
> pseudoprimes"?
> (You say "equivalent condition..." when talking about the primes. Does the
> equivalence require primality?
> Else, where are the differences between the two?)
> If so, then it is maybe better to avoid different names for the same
> sequence
> (although one could say "Might be called NNN in view of ...").
>
> niedz., 30 cze 2019 o 19:23 Tomasz Ordowski napisał(a):
>
> > Maybe someone will find more such new pseudoprimes. Really worth.
> >
>
> Max Alekseyev has added the next two (impressively large) terms to A308963
> about 2 weeks ago.
> (It would be interesting to know how they were found - probably by scanning
> a relevant subsequence of the composite numbers, but it doesn't look as if
> A121707 would be sufficiently discriminative.)
>
> - Maximilian
>
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>