[seqfan] Periodic sequences

[Tomasz Ordowski]

Dear SeqFans!

Let a(n+1) = smallest prime p <> a(n) such that 2^(p-1) == 1 (mod a(n)).

Problem:
Does this recursion give a periodic sequence for each initial term a(1)
being an od prime?

For example: 3, 5, 13, *37, 73, 19,* 37, 73, 19, 37, 73, 19, ...

Best regards,

Thomas Ordowski
_______________
Another example:

17,41,61,181,541,1621,4861,2917,3889,1297,2593,163,*487,**1459,*
487,1459,487,1459,...

Amiram Eldar checked that for any odd prime a(1) < 999, each such sequence
is periodic.