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Search: id:A105875
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| A105875 |
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Primes for which -3 is a primitive root. |
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3
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (djr(AT)nk.ca), Sep 15 2007
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MATHEMATICA
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pr=-3; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]
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CROSSREFS
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Cf. A105874.
Sequence in context: A140556 A003627 A103203 this_sequence A031368 A020613 A135478
Adjacent sequences: A105872 A105873 A105874 this_sequence A105876 A105877 A105878
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Apr 24 2005
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