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Search: id:A055578
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| A055578 |
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"Non-generous primes": primes p whose least positive primitive root is not a primitive root of p^2. |
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+0
8
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OFFSET
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0,1
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COMMENT
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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). The sequence has no other terms p < 2^36.
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REFERENCES
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David Burton, Elementary Number Theory, Allyn and Bacon, Boston, 1976, first edition (cf. Section 8.3).
Stephen Glasby (Stephen.Glasby(AT)cwu.EDU), Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Apr 22, 2001 [found third term].
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LINKS
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Joerg Arndt, Fxtbook
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CROSSREFS
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Cf. A060503, A060504.
Sequence in context: A047076 A030462 A001377 this_sequence A106025 A157959 A094213
Adjacent sequences: A055575 A055576 A055577 this_sequence A055579 A055580 A055581
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KEYWORD
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hard,nonn,bref
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AUTHOR
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Bernard Leak (bernard(AT)brenda-arkle.demon.co.uk), Aug 24 2000
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