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A055578 "Non-generous primes": primes p whose least positive primitive root is not a primitive root of p^2. 8
2, 40487, 6692367337 (list; graph; refs; listen; history; text; internal format)



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).


David Burton, Elementary Number Theory, Allyn and Bacon, Boston, 1976, first edition (cf. Section 8.3).


Table of n, a(n) for n=1..3.

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, Matters Computational (The Fxtbook), section 39.7.2, p.780.


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).


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


Cf. A060503, A060504.

Sequence in context: A228556 A001377 A206854 * A232733 A106025 A157959

Adjacent sequences:  A055575 A055576 A055577 * A055579 A055580 A055581




Bernard Leak (bernard(AT)brenda-arkle.demon.co.uk), Aug 24 2000


a(3) from Stephen Glasby (Stephen.Glasby(AT)cwu.EDU), Apr 22 2001

Edited by Max Alekseyev, Nov 10 2011



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Last modified December 20 11:35 EST 2014. Contains 252241 sequences.