A323590 -id:A323590 - cp's OEIS frontend

A323576 Primes p such that 2 is a primitive root modulo p while 128 is not.

29, 197, 211, 379, 421, 491, 547, 659, 701, 757, 827, 883, 1373, 1499, 1667, 1877, 2213, 2269, 2339, 2437, 2549, 2843, 3011, 3067, 3347, 3557, 3571, 3613, 3851, 3907, 4019, 4229, 4243, 4397, 4621, 4691, 4789, 4957, 5573, 5741, 5923, 6203, 6469, 6637, 6763, 6917

Offset: 1

Jianing Song, Aug 30 2019

nonn

Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) 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).

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.

Cf. A001122, A005596, A000720.

Primes p such that 2 is a primitive root modulo p and that p == 1 (mod q): A307627 (q=3), A307628 (q=5), this sequence (q=7), A323577 (q=11), A323590 (q=13).

forprime(p=3, 7000, if(znorder(Mod(2, p))==(p-1) && p%7==1, print1(p, ", ")))

A323577 Primes p such that 2 is a primitive root modulo p while 2048 is not.

Original entry on oeis.org

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

Jianing Song, Aug 30 2019

nonn

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).

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.

Cf. A001122, A005596, A000720.

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).

forprime(p=3, 12000, if(znorder(Mod(2, p))==(p-1) && p%11==1, print1(p, ", ")))

cp's OEIS Frontend

A323576 Primes p such that 2 is a primitive root modulo p while 128 is not.

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