3,5,11 - sequence /proposal for an additional definition

[Gottfried Helms]

Seqfans -

 1) a few stupid typing errors, sorry. But it doesn't
    spoil the meaning too terribly, so I'll just leave it as it was.

 2) The matter can be simplified:
    the inf-hyperroot n^^°° = a (mod p) can more simply be
    expressed as

     n^a = a  (mod p)

 and so we ask, whether in the residue-group of p an "n"
 exists with that property, or in other words:

   whether there exists an "n" which can be expressed as
   the a'th root of a.

 The number of solutions n for a given p seems to increase
 with p, and is even higher if p is not prime but composite.

 There is always a "trivial" solution, for n=1 (mod p) (obvious).

 The sequence 3,5,11 is then
  the sequence of primes>2, which have a non-trivial element "n"
  where n^a = a (mod p, a integer >0)

 (which may be of a certain interest; maybe one can find
  a connection with some analogs to the Lucas-Lehmer-test
  or similar)

Regards -

Gottfried Helms