A301913 Primes which divide numbers of the form 3^k + 2 for k >= 1.

5, 7, 11, 17, 19, 29, 31, 43, 53, 59, 79, 83, 89, 97, 101, 107, 113, 127, 131, 137, 139, 149, 163, 173, 179, 197, 199, 211, 223, 227, 233, 241, 251, 257, 269, 281, 283, 293, 317, 331, 337, 347, 353, 379, 389, 401, 409, 419, 439, 443, 449, 457, 461, 463, 467

Offset: 1

Author

Luke W. Richards, Mar 28 2018

Keywords

• nonn

Comments

The first odd prime not to appear in the sequence is 3 because 3^k + 2 == 2 mod 3 for k >= 1.

Primes p such that the order of -2 (mod p) divides the order of 3 (mod p). - Joerg Arndt, Mar 31 2018, corrected by Robert Israel, May 04 2018

Examples

			5 divides 245 which is 3^5+2 so 5 is in the sequence.
7 divides 245 which is 3^5+2 so 7 is in the sequence.
The values of x = (3^k+2) mod 13 for k = 0, 1, 2, 3, ... are 3, 5, 11, 3, 5, 11, ...; 13 never divides any 3^k + 2, so 13 is not in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A168607.

Programs

Maple

select(t -> numtheory:-mlog(-2,3,t)<>FAIL, [seq(ithprime(i),i=3..100)]);

Mathematica

fQ[p_] := IntegerQ@ MultiplicativeOrder[3, p, -2]; Select[ Prime@ Range@ 100, fQ] (* Robert G. Wilson v, Apr 07 2018 *)

PARI

is(n)=n>4 && isprime(n) && znorder(Mod(-2,n))%znorder(Mod(3,n))==0 \\ Charles R Greathouse IV, May 04 2018