

A105875


Primes for which 3 is a primitive root.


4



2, 5, 11, 17, 23, 29, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 443, 449, 461, 467, 479, 503, 509, 521, 557, 563, 569, 587, 593, 599, 617, 641
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OFFSET

1,1


COMMENTS

Also, primes for which 27 is a primitive root. Proof: 27 = (3)^3, so 27 is a primitive root just when 3 is a primitive root and the prime is not 3k+1. Now if 3 is a primitive root, then 3 is not a quadratic residue and so the prime is not 3k+1.  Don Reble, Sep 15 2007


LINKS



MATHEMATICA

pr=3; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #1 &]


PROG

(Python)
from sympy import n_order, nextprime
from itertools import islice
def A105875_gen(startvalue=2): # generator of terms >= startvalue
p = max(startvalue1, 1)
while (p:=nextprime(p)):
if p!=3 and n_order(3, p) == p1:
yield p


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



