[seqfan] Re: Question from Harvey Dale about A233552

[Hugo Pfoertner]

As Don Reble has shown, all current terms of A233552 can be proved to be in
the sequence using covering sets with small moduli. Since squares are not
excluded by the definition, they have to be added. A correspondingly
enhanced version of A233552 will be 25, 49, 121, 169, 289, 361, 529, 625,
841, 919, 961, 1225, 1369, 1681, 1849, 2209, 2401, 2419, 2629, 2809, 3025,
3301, 3481, 3721
For a continuation from there onward (3991), (4225), 4489, 5041, 5209,
5329, .. without the ()-terms, we need to find primes of the form
(3991*4^k-1)/3, (4225*4^k-1)/3.

Similarly, all current terms of A233551 can be shown to be members of the
sequence using a covering set with small moduli. A case similar to 15661 in
A233552 is 11429 needing other moduli than the remaining terms.
A potentially modified sequence will be identical to A233551 in the initial
terms, (none missing)
419, 659, 1769, 2609, 2651, 2981,
but to continue, primes of the form (3719*4^k+1)/3 and (5459*4^k+1)/3 have
to be found. k<=20000 is already checked.
To confirm the correctness of the current version of A233551 through
a(n)=10000, primes of the form (n*4^k+1)/3 have also to be found for
n=6971, 7229, 8447, 9521, 9791.

On Mon, May 27, 2019 at 3:50 PM Neil Sloane <njasloane at gmail.com> wrote:

> For A233552, I have added a strong warning that the entry is horribly
> wrong.
>
> There has been a lot of discussion here.  Could someone give a summary?
> What is the correct start of the sequence?  How many initial terms can we
> say for certain are correct?
>
> Same question for A233551.
>
> 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 Mon, May 27, 2019 at 7:12 AM Hugo Pfoertner <yae9911 at gmail.com> wrote:
>
> > Found an "easy" answer myself: 2495 is not in the sequence because
> > (2495*4^17121+1)/3 is (pseudo)prime. One might be less lucky for other
> > candidates like 3419, 3719, 5459, 5837, 8447, 9521, ...
> >
> > On Mon, May 27, 2019 at 12:51 PM Hugo Pfoertner <yae9911 at gmail.com>
> wrote:
> >
> > > For http://oeis.org/A233551 an example "2495 is not in the sequence
> > > because ...." would definitely help to understand the construction.
> Until
> > > that is provided, the sequence deserves the keyword "obsc", at least in
> > my
> > > opinion.
> > >
> >
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> >
>
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