A225888 Primes p such that neither 2 nor 3 are primitive roots, but together 2 and 3 generate the nonzero residues mod p.

41, 103, 109, 151, 157, 229, 251, 271, 277, 367, 397, 683, 733, 761, 967, 971, 991, 1051, 1069, 1163, 1181, 1289, 1303, 1429, 1471, 1543, 1759, 1783, 1789, 1811, 1879, 2003, 2297, 2411, 2441, 2551, 2749, 2791, 2887, 2917, 3061, 3079, 3109, 3229, 3251, 3301, 3319

Offset: 1

Author

John L. Drost, May 19 2013

Keywords

• nonn

Examples

			2 has multiplicative order 20 mod 41, 3 has order 8 mod 41 so neither is a primitive root. The subgroup 2 and 3 generate together will have order lcm(20,8) = 40 so 2 and 3 generate all nonzero residues.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001122, A001123.

Programs

PARI

is(n)=if(n>40 && isprime(n), my(a=znorder(Mod(2,n)),b); if(a==n-1,return(0)); b=znorder(Mod(3,n)); bCharles R Greathouse IV, May 19 2013