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

[Allan Wechsler]

I didn't closely follow the argument about A361831 (I assume we are talking
about the first incarnation, for Braxton, not the second one for Israel).
But it looks like the problem was one of well-definedness. They could not
prove the value of the A(26), and it would have been weird to have a
sequence with only 25 terms, with any extension depending on a
theoretical breakthrough.

It doesn't look like your sequence has that impediment. You say you have
several thousand terms. I admit that the sequence doesn't seem all that
mathematically interesting *to me*, but this is purely a matter of taste
and OEIS has happily accepted sequences much *less* interesting (again, to
me). So I would say to submit it. (I did try Superseeker, and it came up
blank.)

Note that this sequence would contain no 2's, because if n+F(2) is prime,
then n+F(1) is the same prime.

On Mon, Mar 27, 2023 at 9:21 PM Pontus von Brömssen <
pontus.von.bromssen at gmail.com> wrote:

> 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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