[seqfan] Re: Question from Harvey Dale about A233552

[M. F. Hasler]

Maybe it could be interesting to have a "companion sequence" of "proofs",
like e.g.,
b(n) = the least exponent k which leads to a prime (n*4^k-1)/3,
or -p where p is the least possible largest prime of a covering set proving
that no such k exists for n,
or 0 if none of the above exist (? can this happen ?).

- Maximilian

On Tue, May 28, 2019 at 6:43 AM Hugo Pfoertner <yae9911 at gmail.com> wrote:

> Just for clarification: 3145 is eliminated by (3145*4^39870-1)/3 being a
> (pseudo)prime. Therefore in a sequence for replacement of A233552 the first
> term with unknown status is at the moment 3991 (no primes through k=27000).
> 6019 and 8869 also lead to primes and may be dropped from the list of
> numbers with unknown status.
>
> On Tue, May 28, 2019 at 2:36 AM David Radcliffe <dradcliffe at gmail.com>
> wrote:
>
> > All of the terms listed in A233552 are correct, but many are missing.
> Here
> > are the correct initial terms for A233552:
> > 25, 49, 121, 169, 289, 361, 529, 625, 841, 919, 961, 1225, 1369, 1681,
> > 1849, 2209, 2401, 2419, 2629, 2809, 3025
> >
> > All numbers of the form (6k + 1)^2 or (6k - 1)^2 with k >= 1 are terms.
> >
> > The following numbers are terms because they have covering sets of prime
> > divisors:
> > 919, 2419, 2629, 3301, 5209, 5539, 5581, 6421, 7771, 8551, 9109, 9871,
> > 10039, 10819, 11491, 13399, 13729, 13771, 14611, 15661, 15961, 16741,
> > 17299, 18061, 18229, 18799, 19009, 19681, 21589, 21919, 21961, 24151,
> > 24931, 25489
> >
> > The covering set for 15661 is {3,5,7,17,241}. For the rest, {3,5,7,11,13}
> > is a covering set, not necessarily minimal.
> >
> > The following numbers have unknown status. For each n in this list, I
> have
> > not found k < 10000 such that (n*4^k-1)/3 is a pseudoprime, nor have I
> > found a covering set.
> >
> > 3145, 3991, 5461, 6019, 7309, 8869, 12091, 14701, 18439, 19651, 20569,
> > 21289, 21781, 22171, 22285, 22519, 22789, 22891
> >
>