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

[Allan Wechsler]

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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