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

[Robert Gerbicz]

"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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