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

Gottfried Helms Annette.Warlich at t-online.de
Tue Nov 8 22:13:06 CET 2005

```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

```