[seqfan] What would you call this recurrence relation?

[Alonso Del Arte]

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, ...

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

Al