

A019338


Primes with primitive root 8.


5



3, 5, 11, 29, 53, 59, 83, 101, 107, 131, 149, 173, 179, 197, 227, 269, 293, 317, 347, 389, 419, 443, 461, 467, 491, 509, 557, 563, 587, 653, 659, 677, 701, 773, 797, 821, 827, 941, 947, 1019, 1061, 1091, 1109, 1187, 1229, 1259, 1277, 1283, 1301, 1307, 1373, 1427
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OFFSET

1,1


COMMENTS

Members of A001122 that are not congruent to 1 mod 3.  Robert Israel, Aug 12 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for primes by primitive root


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,3)==1.  Gerry Martens, May 15 2015
On Artin's conjecture, a(n) ~ (5/3A) n log n, where A = A005596 is Artin's constant.  Charles R Greathouse IV, May 21 2015


MAPLE

select(t > isprime(t) and numtheory:order(8, t) = t1, [2*i+1 $ i=1..1000]); # Robert Israel, Aug 12 2014


MATHEMATICA

pr=8; Select[Prime[Range[200]], 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[#, 3], 20]]==1 &]+1
(* Gerry Martens, Apr 28 2015 *)


PROG

(PARI) is(n)=isprime(n) && n>2 && znorder(Mod(8, n))==n1 \\ Charles R Greathouse IV, May 21 2015


CROSSREFS

Sequence in context: A093706 A109945 A045536 * A046134 A177932 A213210
Adjacent sequences: A019335 A019336 A019337 * A019339 A019340 A019341


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



