[seqfan] Re: Question from Harvey Dale about A233552

[Neil Sloane]

Don't much like that idea.  Look at the link in A233551, which has a claim
by Wesolowski that
(419*22n + 1)/3 can never be prime
<https://primes.utm.edu/glossary/xpage/Prime.html>. [Wesolowski
<https://primes.utm.edu/curios/ByOne.php?submitter=Wesolowski>]
What is the proof?
We need to find a number-theorist who can straighten this out.

Adding a bound on k is not an acceptable solution, imho!

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 Sun, May 26, 2019 at 3:26 PM Hugo Pfoertner <yae9911 at gmail.com> wrote:

> http://oeis.org/A233551 shows a similar deficiency, i.e., there are
> candidate terms missing in the sequence passing a test deliberately
> truncated at k=10000
> 2495, 3419, 3719, 5459, 5837,....
> One could modify the definition of A233551 and A233552 by introducing an
> upper limit for k, e.g. 1<=k<=n, and then add all missing terms.
> A233552 would become
> 25, 49, 121, 169, 289, 361, 373, 499, 529, 625, 751, 841, 919, 961, 1159,
> 1171, 1189, 1225, 1369, 1681, 1849, 2209, 2401, 2419, 2629, 2809, 3025,
> 3061, 3145, 3301, 3445, 3481, 3721, 3943, 3991, 4159, 4225, 4489, 5041,
> 5209, 5329, 5461, 5539, 5581,
>
> A233551 would become
> 89, 419, 659, 839, 1769, 2495, 2609, 2651, 2981, 3419, 3719, 4889, 5459,
> 5561, 5771, 5837, 6341, 6509, 6971, 7271, 7829, 8447, 8609, 9521,
> with 89 and 839 not passing a "for all k" condition.
>
>
> On Sun, May 26, 2019 at 7:31 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > Harvey just asked me the following question.  Can anyone help?
> >
> >
> > I may be missing something, but there seem to be many terms missing from
> > the above sequence. My calculations show that, up to 1000, each of 25,
> 49,
> > 121, 169, 289, 361, 373, 499, 529, 613, 625, 751, 841, 919, and 961
> > satisfies the definition, but only 361 and 919 appear in the data. Am I
> > overlooking something? Also, I’m not sure how to test “all k >=1” because
> > that would require going up to infinity — so, is there some top limit to
> > the value of k that should be tested, e.g., k<=n? Or is there some other
> > way to do the test that doesn’t require generating lots of terms?
> >
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> >
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