A323617 -id:A323617 - cp's OEIS frontend

A323594 Primes p such that 3 is a primitive root modulo p while 27 is not.

7, 19, 31, 43, 79, 127, 139, 163, 199, 211, 223, 283, 331, 379, 463, 487, 571, 607, 631, 691, 739, 751, 811, 823, 859, 907, 1039, 1063, 1087, 1123, 1231, 1279, 1291, 1327, 1423, 1447, 1459, 1483, 1567, 1579, 1627, 1663, 1699, 1723, 1747, 1831, 1951, 1987, 1999

Offset: 1

Jianing Song, Aug 30 2019

nonn

Primes p such that 3 is a primitive root modulo p (i.e., p is in A019334) and that p == 1 (mod 3).

According to Artin's conjecture, the number of terms <= N is roughly ((2/5)*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).

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Artin's constant.
Wikipedia, Artin's conjecture on primitive roots.

Complement of A019353 with respect to A019334.
Cf. also A005596, A000720.
Primes p such that 3 is a primitive root modulo p and that p == 1 (mod q): this sequence (q=3), A323617 (q=5), A323628 (q=7).

forprime(p=5, 2000, if(znorder(Mod(3, p))==(p-1) && p%3==1, print1(p, ", ")))

A323628 Primes p such that 3 is a primitive root modulo p while 2187 is not.

Original entry on oeis.org

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

Jianing Song, Aug 30 2019

nonn

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).

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Artin's constant
Wikipedia, Artin's conjecture on primitive roots

Cf. A019334, A005596, A000720.

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).

select(p -> isprime(p) and numtheory:-order(3,p)=p-1, [seq(i,i=1..10000,7)]); # Robert Israel, Sep 01 2019

forprime(p=5, 5500, if(znorder(Mod(3, p))==(p-1) && p%7==1, print1(p, ", ")))

cp's OEIS Frontend

A323594 Primes p such that 3 is a primitive root modulo p while 27 is not.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI