|
| |
|
|
A055578
|
|
"Non-generous primes": primes p whose least positive primitive root is not a primitive root of p^2.
|
|
8
| | |
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| For r a primitive root of a prime p, r + qp is a primitive root of p: but r + qp is also a primitive root of p^2, except for q in some unique residue class modulo p. In the exceptional case, r + qp has order p-1 modulo p^2 (Burton, section 8.3).
No other terms below 10^12 (Paszkiewicz, 2009).
|
|
|
REFERENCES
| David Burton, Elementary Number Theory, Allyn and Bacon, Boston, 1976, first edition (cf. Section 8.3).
|
|
|
LINKS
| Stephen Glasby, Three questions about the density of certain primes, Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Apr 22, 2001.
A. Paszkiewicz A new prime for which the least primitive root (mod p) and the least primitive root (mod p^2) are not equal, Math. Comp. 78 (2009), 1193-1195.
Joerg Arndt, Fxtbook.
|
|
|
FORMULA
| Prime A000040(n) is in this sequence iff A001918(n)^(A000040(n)-1) == 1 (mod A000040(n)^2).
Prime A000040(n) is in this sequence iff A001918(n) differs from A127807(n).
|
|
|
CROSSREFS
| Cf. A060503, A060504.
Sequence in context: A030462 A001377 A206854 * A106025 A157959 A094213
Adjacent sequences: A055575 A055576 A055577 * A055579 A055580 A055581
|
|
|
KEYWORD
| hard,nonn,bref,more
|
|
|
AUTHOR
| Bernard Leak (bernard(AT)brenda-arkle.demon.co.uk), Aug 24 2000
|
|
|
EXTENSIONS
| a(3) from Stephen Glasby (Stephen.Glasby(AT)cwu.EDU), Apr 22 2001
Edited by Max Alekseyev (maxale(AT)gmail.com), Nov 10 2011
|
| |
|
|
