[seqfan] Re: Add a Fibonacci number to get a prime

[Neil Sloane]

 Alois Heinz agrees that Braxton's sequence is interesting, so I have
created A361509 and A361510 for it.
Pontus, can you go ahead now and create your version, and email me the
A-number?  (By the way, I apologize for misspelling your name the other
day.)

Once all three sequences have been approved, I will contact Jack Braxton
and apologize.

There were programs for the original version of his sequence in MMA and
PARI, but they did not match the version I am using, so I did not copy them
over.  I also did not indicate how far people searched for a(26), but that
should be added.

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com



On Wed, Mar 29, 2023 at 12:08 AM Neil Sloane <njasloane at gmail.com> wrote:

> I can get in touch with Jack Braxton, yes.  But before we proceed any
>  further, I want to consult the editors who rejected his original version,
> and make sure they agree to having it in the OEIS.
>
> I will report here when I hear back from them.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Tue, Mar 28, 2023 at 11:45 PM Allan Wechsler <acwacw at gmail.com> wrote:
>
>> Do we have a way to get back in touch with Jack Braxton to get him to
>> resubmit?
>>
>> On Tue, Mar 28, 2023 at 9:51 AM Neil Sloane <njasloane at gmail.com> wrote:
>>
>> > Well, I think we should certainly try to rescue Braxton's sequence.
>> There
>> > should be two sequences, one giving the actual Fibonacci numbers, as in
>> his
>> > original submission, and one giving their indices.  Using essentially
>> his
>> > definition, with -1 if no such Fibonacci number exists, I don't see any
>> > problem.  We just stop at the 25th term, until such time as someone
>> proves
>> > that a(26) exists or does not exist.  Does that sound reasonable?
>> > Best regards
>> > Neil
>> >
>> > Neil J. A. Sloane, Chairman, OEIS Foundation.
>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>> > Email: njasloane at gmail.com
>> >
>> >
>> >
>> > On Tue, Mar 28, 2023 at 9:11 AM Allan Wechsler <acwacw at gmail.com>
>> wrote:
>> >
>> > > In that case, modify the definition to be -1 in the case that n +
>> F(k) is
>> > > always composite. We still don't run into the philosophical difficulty
>> > > encountered by Braxton, because we can use techniques like Robert
>> > > Gerbicz's to *prove* the fact. (In fact this technique could rescue
>> > Braxton
>> > > as well.)
>> > >
>> > > On Tue, Mar 28, 2023 at 6:40 AM Robert Gerbicz <
>> robert.gerbicz at gmail.com
>> > >
>> > > wrote:
>> > >
>> > > > "An informal probabilistic argument indicates that a(n) exists for
>> all
>> > > n."
>> > > >
>> > > > It is a false conjecture. Say for n=14475 for every k
>> > > > 14475+fibonacci(k) is composite!
>> > > >
>> > > > Could be the smallest such n value, but really not checked.
>> > > >
>> > > > Set T=2*3*5*7*11*23*31=1647030, then the Fibonacci sequence is
>> periodic
>> > > mod
>> > > > T using period=240.
>> > > > So need to check only the first 240 Fibonacci numbers, and for
>> > > > each of them T and 14475+fibonacci(k) is not coprime, and of course
>> > > bigger
>> > > > than 31, so 14475+fibonacci(k) is composite for the first 240 k
>> values,
>> > > but
>> > > > then for every k.
>> > > >
>> > > > Pontus von Brömssen <pontus.von.bromssen at gmail.com> ezt írta
>> (időpont:
>> > > > 2023. márc. 28., K, 3:21):
>> > > >
>> > > > > I played around with the idea of the recently rejected sequence
>> > A361831
>> > > > > (see version #29) and came up with the following variant. Let
>> a(n) be
>> > > the
>> > > > > smallest k such that n+Fibonacci(k) is prime. The sequence starts
>> > (from
>> > > > > n=0): 3, 1, 0, 0, 1, 0, 1, 0, 4, 3, 1. For example, the first
>> > Fibonacci
>> > > > > number F such that 8+F is prime is F=3=Fibonacci(4), so a(8)=4.
>> > > > >
>> > > > > An informal probabilistic argument indicates that a(n) exists for
>> all
>> > > n.
>> > > > An
>> > > > > example where a(n) gets fairly large is a(6313)=25224. (The
>> > > corresponding
>> > > > > prime 6313+F(25224) has 5272 digits.)
>> > > > >
>> > > > > Considering that a closely related sequence was rejected, is this
>> > > > sequence
>> > > > > worth submitting?
>> > > > >
>> > > > > Best regards,
>> > > > >
>> > > > > Pontus
>> > > > >
>> > > > > --
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>> > > > >
>> > > >
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