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.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Wikipedia, Artin's conjecture on primitive roots
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 24 2005
STATUS
approved