

A055578


"Nongenerous primes": primes p whose least positive primitive root is not a primitive root of p^2.


10




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 p1 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

Table of n, a(n) for n=1..3.
Joerg Arndt, Matters Computational (The Fxtbook), section 39.7.2, p.780.
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), 11931195.


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).


MATHEMATICA

Select[Prime@Range[7!], ! PrimitiveRoot[#] == PrimitiveRoot[#^2] &] (* Arkadiusz Wesolowski, Sep 06 2012 *)


CROSSREFS

Cf. A060503, A060504.
Sequence in context: A291881 A257968 A303738 * A232733 A106025 A157959
Adjacent sequences: A055575 A055576 A055577 * A055579 A055580 A055581


KEYWORD

hard,nonn,bref,more,changed


AUTHOR

Bernard Leak (bernard(AT)brendaarkle.demon.co.uk), Aug 24 2000


EXTENSIONS

a(3) from Stephen Glasby (Stephen.Glasby(AT)cwu.EDU), Apr 22 2001
Edited by Max Alekseyev, Nov 10 2011


STATUS

approved



