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%I #21 Nov 15 2017 04:59:30
%S 41,103,109,151,157,229,251,271,277,367,397,683,733,761,967,971,991,
%T 1051,1069,1163,1181,1289,1303,1429,1471,1543,1759,1783,1789,1811,
%U 1879,2003,2297,2411,2441,2551,2749,2791,2887,2917,3061,3079,3109,3229,3251,3301,3319
%N Primes p such that neither 2 nor 3 are primitive roots, but together 2 and 3 generate the nonzero residues mod p.
%H Charles R Greathouse IV, <a href="/A225888/b225888.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%o (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
%Y Cf. A001122, A001123.
%K nonn
%O 1,1
%A _John L. Drost_, May 19 2013
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