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A323577
Primes p such that 2 is a primitive root modulo p while 2048 is not.
3
67, 419, 661, 859, 947, 1123, 1277, 1453, 2069, 2267, 2333, 2531, 2707, 2861, 3037, 3323, 3499, 3851, 3917, 4093, 4357, 4621, 4973, 5171, 5501, 6029, 6469, 6491, 6733, 7019, 7283, 7349, 7459, 7547, 7789, 7877, 8053, 8669, 8867, 8933, 9901, 9923, 10099, 10253, 10891, 10979
OFFSET
1,1
COMMENTS
Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) and that p == 1 (mod 11).
According to Artin's conjecture, the number of terms <= N is roughly ((10/109)*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=3, 12000, if(znorder(Mod(2, p))==(p-1) && p%11==1, print1(p, ", ")))
CROSSREFS
Primes p such that 2 is a primitive root modulo p and that p == 1 (mod q): A307627 (q=3), A307628 (q=5), A323576 (q=7), this sequence (q=11), A323590 (q=13).
Sequence in context: A142371 A142609 A262344 * A142735 A342803 A219736
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 30 2019
STATUS
approved