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

[Allan Wechsler]

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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