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A323617
Primes p such that 3 is a primitive root modulo p while 243 is not.
3
31, 101, 211, 281, 331, 401, 461, 521, 571, 631, 641, 691, 701, 751, 811, 821, 881, 941, 1061, 1231, 1291, 1301, 1361, 1481, 1601, 1721, 1831, 1901, 1951, 2011, 2081, 2141, 2311, 2371, 2381, 2731, 2741, 2801, 2861, 3041, 3271, 3331, 3391, 3461, 3571, 3581, 3701, 3761, 3821, 3931
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 5).
According to Artin's conjecture, the number of terms <= N is roughly ((4/19)*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.
PROG
(PARI) forprime(p=5, 4000, if(znorder(Mod(3, p))==(p-1) && p%5==1, print1(p, ", ")))
CROSSREFS
Primes p such that 3 is a primitive root modulo p and that p == 1 (mod q): A323594 (q=3), this sequence (q=5), A323628 (q=7).
Sequence in context: A187517 A039463 A181188 * A142096 A268986 A222550
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 30 2019
STATUS
approved