

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))==n1 \\ 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



