[seqfan] Re: What would you call this recurrence relation?

Max Alekseyev maxale at gmail.com
Fri Mar 29 05:59:11 CET 2013


On Thu, Mar 28, 2013 at 11:35 PM, Alonso Del Arte
<alonso.delarte at gmail.com> wrote:
> Choose a prime p, say p = 2. What is the smallest prime q such that p + 1
> divides q - 1 and p - 1 divides q + 1 ? (The latter part of the question is
> trivial for now). That would be 7.
>
> Then reset p = 7 and find the corresponding q. That's 17. And so on and so
> forth, giving 2, 7, 17, 127, 7937, ...

In other words, starting from p=7, we have q == -p (mod (p^2 - 1)/2).
I suspect, for many terms we may simply have q = (p^2 - 1)/2 - p, at
least all listed terms are such.

> What would this recurrence relation be called? If it can be called a
> recurrence relation in the first place?

Not every recurrence relation has a special name.

Regards,
Max



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