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%I #29 Mar 31 2024 15:03:28
%S 5,23,29,47,53,71,101,149,167,173,191,197,239,263,269,293,311,317,359,
%T 383,389,461,479,503,509,557,599,647,653,677,701,719,743,773,797,821,
%U 839,863,887,941,983,1031,1061,1109,1151,1223,1229,1277,1301,1319,1367,1373,1439
%N Primes for which -8 is a primitive root.
%H Vincenzo Librandi, <a href="/A105880/b105880.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%F 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
%t pr=-8; Select[Prime[Range[400]], MultiplicativeOrder[pr, # ] == #-1 &] (* _N. J. A. Sloane_, Jun 01 2010 *)
%t a[p_, q_]:= Sum[2 Cos[2^n Pi/((2 q+1)(2 p+1))],{n,1,2 q p}]
%t 2 Select[Range[800], Rationalize[N[a[#, 9], 20]] == 1 &] + 1
%t (* _Gerry Martens_, Apr 28 2015 *)
%o (PARI) is(n)=isprime(n) && n>3 && znorder(Mod(-8,n))==n-1 \\ _Charles R Greathouse IV_, May 21 2015
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Apr 24 2005
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