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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

LINKS

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

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

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 December 7 13:07 EST 2016. Contains 278875 sequences.