# [seqfan] Re: Sequence A019334

Joerg Arndt arndt at jjj.de
Wed Jun 17 06:00:00 CEST 2009

```I'd suggest to leave 2 in and add a comment.

* David Wilson <davidwwilson at comcast.net> [Jun 17. 2009 13:38]:
> n is a primitive root of p if n generates all the nonzero residues modulo p.
>
> In the case p = 2, the primitive root 1 generates all residues modulo 2. But so does 3 or any odd number, which are all congruent to 1 (mod 2).
>
> In the general case, if r is a primitive root of prime p, then r+pk is also a primitive root of p.
>
> In most treatments of primitive roots of p, the context is modulo p arithmetic, so primitive roots of p are generally considered residues modulo p, which are expressed by numbers less than p. If we honor that convention, 3 would not be considered a primitive root of 2.
>
> So I will leave it to seqfan (Neil) as to whether values >= p should be considered primitive roots of p with regard to the sequences in question.
>
> ----- Original Message -----
>   From: Harry J. Smith
>   To: davidwwilson at comcast.net
>   Sent: Tuesday, June 16, 2009 12:22 PM
>   Subject: Sequence A019334
>
>
>   David:
>
>
>
>   Why do you have 2 in Sequence A019334, Primes with primitive root 3?
>
>   The prime number 2 has 1 primitive root equal to 1.
>
>
>
>   I have the same question about A019335, A019337, A019339, ., A019421
>
>
>
>   -Harry
> [...]

```