A105875 - OEIS

A105875

Primes for which -3 is a primitive root.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for primes by primitive root

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(startvalue-1, 1)

while (p:=nextprime(p)):