[seqfan] Re: Question from Harvey Dale about A233552

[Hugo Pfoertner]

Needed for an extension of a corrected version of A233552: Are there primes
of the form (n*4^k-1)/3 for n = 3991, 5461, 6019, 7309, 8869 ? None found
for k<=10000. 4225=square does not belong to this list.

On Mon, May 27, 2019 at 7:37 PM Hugo Pfoertner <yae9911 at gmail.com> wrote:

> 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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>