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 A105880 Primes for which -8 is a primitive root. 3
 5, 23, 29, 47, 53, 71, 101, 149, 167, 173, 191, 197, 239, 263, 269, 293, 311, 317, 359, 383, 389, 461, 479, 503, 509, 557, 599, 647, 653, 677, 701, 719, 743, 773, 797, 821, 839, 863, 887, 941, 983, 1031, 1061, 1109, 1151, 1223, 1229, 1277, 1301, 1319, 1367, 1373, 1439 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Jianing Song, May 12 2024: (Start) Members of A105874 that are not congruent to 1 mod 3. Terms are congruent to 5 or 23 modulo 24. According to Artin's conjecture, the number of terms <= N is roughly ((3/5)*C)*PrimePi(N), where C is the Artin's constant = A005596, PrimePi = A000720. Compare: the number of terms of A001122 that are no greater than N is roughly C*PrimePi(N). (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Wikipedia, Artin's conjecture on primitive roots Index entries for primes by primitive root FORMULA Let a(p,q)=sum(n=1,2*p*q,2*cos(2^n*Pi/((2*q+1)*(2*p+1)))). Then 2*p+1 is a prime of this sequence when a(p,9)==1. - Gerry Martens , May 21 2015 MATHEMATICA pr=-8; Select[Prime[Range[400]], MultiplicativeOrder[pr, # ] == #-1 &] (* N. J. A. Sloane, Jun 01 2010 *) a[p_, q_]:= Sum[2 Cos[2^n Pi/((2 q+1)(2 p+1))], {n, 1, 2 q p}] 2 Select[Range[800], Rationalize[N[a[#, 9], 20]] == 1 &] + 1 (* Gerry Martens, Apr 28 2015 *) PROG (PARI) is(n)=isprime(n) && n>3 && znorder(Mod(-8, n))==n-1 \\ Charles R Greathouse IV, May 21 2015 CROSSREFS Cf. A105874, A005596, A000720. Sequence in context: A243458 A067367 A140386 * A163587 A038922 A019367 Adjacent sequences: A105877 A105878 A105879 * A105881 A105882 A105883 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 24 2005 STATUS approved

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Last modified September 18 08:48 EDT 2024. Contains 375999 sequences. (Running on oeis4.)