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A323628
Primes p such that 3 is a primitive root modulo p while 2187 is not.
3
29, 43, 113, 127, 197, 211, 281, 379, 449, 463, 617, 631, 701, 953, 1373, 1709, 1723, 2129, 2143, 2213, 2311, 2381, 2549, 2633, 2647, 2731, 2801, 2969, 3137, 3389, 3557, 3571, 3823, 4159, 4229, 4243, 4327, 4397, 4481, 4649, 4663, 4817, 4831, 4999, 5237, 5419
OFFSET
1,1
COMMENTS
Primes p such that 3 is a primitive root modulo p (i.e., p is in A019334) and that p == 1 (mod 7).
According to Artin's conjecture, the number of terms <= N is roughly ((6/41)*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).
LINKS
Eric Weisstein's World of Mathematics, Artin's constant
MAPLE
select(p -> isprime(p) and numtheory:-order(3, p)=p-1, [seq(i, i=1..10000, 7)]); # Robert Israel, Sep 01 2019
PROG
(PARI) forprime(p=5, 5500, if(znorder(Mod(3, p))==(p-1) && p%7==1, print1(p, ", ")))
CROSSREFS
Primes p such that 3 is a primitive root modulo p and that p == 1 (mod q): A323594 (q=3), A323617 (q=5), this sequence (q=7).
Sequence in context: A043171 A043951 A042973 * A020997 A108280 A374009
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 30 2019
STATUS
approved