This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105880 #32 May 13 2024 00:06:59
%S A105880 5,23,29,47,53,71,101,149,167,173,191,197,239,263,269,293,311,317,359,
%T A105880 383,389,461,479,503,509,557,599,647,653,677,701,719,743,773,797,821,
%U A105880 839,863,887,941,983,1031,1061,1109,1151,1223,1229,1277,1301,1319,1367,1373,1439
%N A105880 Primes for which -8 is a primitive root.
%C A105880 From _Jianing Song_, May 12 2024: (Start)
%C A105880 Members of A105874 that are not congruent to 1 mod 3. Terms are congruent to 5 or 23 modulo 24.
%C A105880 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)
%H A105880 Vincenzo Librandi, <a href="/A105880/b105880.txt">Table of n, a(n) for n = 1..1000</a>
%H A105880 Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots">Artin's conjecture on primitive roots</a>
%H A105880 <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%F A105880 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 A105880 pr=-8; Select[Prime[Range[400]], MultiplicativeOrder[pr, # ] == #-1 &] (* _N. J. A. Sloane_, Jun 01 2010 *)
%t A105880 a[p_, q_]:= Sum[2 Cos[2^n Pi/((2 q+1)(2 p+1))],{n,1,2 q p}]
%t A105880 2 Select[Range[800], Rationalize[N[a[#, 9], 20]] == 1 &] + 1
%t A105880 (* _Gerry Martens_, Apr 28 2015 *)
%o A105880 (PARI) is(n)=isprime(n) && n>3 && znorder(Mod(-8,n))==n-1 \\ _Charles R Greathouse IV_, May 21 2015
%Y A105880 Cf. A105874, A005596, A000720.
%K A105880 nonn
%O A105880 1,1
%A A105880 _N. J. A. Sloane_, Apr 24 2005