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

1,1

Links

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

Example

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.

Prog

(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)); b<n-1 && lcm(a, b)==n-1, 0) \\ Charles R Greathouse IV, May 19 2013

Crossrefs

Cf. A001122, A001123.

Sequence in context: A309934 A126588 A142794 * A156971 A123043 A142014

Adjacent sequences: A225885 A225886 A225887 * A225889 A225890 A225891

Keyword

nonn

Author

John L. Drost, May 19 2013

Status

approved