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 A105875 Primes for which -3 is a primitive root. 4
 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; refs; listen; history; text; internal format)
 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 Index entries for primes by primitive root MATHEMATICA pr=-3; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &] PROG (Python) from sympy import n_order, nextprime from itertools import islice def A105875_gen(startvalue=2): # generator of terms >= startvalue p = max(startvalue-1, 1) while (p:=nextprime(p)): if p!=3 and n_order(-3, p) == p-1: yield p A105875_list = list(islice(A105875_gen(), 20)) # Chai Wah Wu, Aug 11 2023 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

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Last modified June 19 03:10 EDT 2024. Contains 373492 sequences. (Running on oeis4.)