

A105875


Primes for which 3 is a primitive root.


3



2, 5, 11, 17, 23, 29, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 443, 449, 461, 467, 479, 503, 509, 521, 557, 563, 569, 587, 593, 599, 617, 641
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OFFSET

1,1


COMMENTS

Also, primes for which 27 is a primitive root. Proof: 27 = (3)^3, so 27 is a primitive root just when 3 is a primitive root and the prime is not 3k+1. Now if 3 is a primitive root, then 3 is not a quadratic residue and so the prime is not 3k+1.  Don Reble, Sep 15 2007


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


MATHEMATICA

pr=3; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #1 &]


CROSSREFS

Cf. A105874.
Sequence in context: A140556 A003627 A103203 * A031368 A020613 A135478
Adjacent sequences: A105872 A105873 A105874 * A105876 A105877 A105878


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 24 2005


STATUS

approved



