[seqfan] Re: Question from Harvey Dale about A233552

[Fred Lunnon]

For     "(419*22n + 1)/3 can never be prime"
read   "(419*2^(2n) + 1)/3 can never be prime"

WFL



On 5/26/19, Neil Sloane <njasloane at gmail.com> wrote:
> 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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