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%I #26 May 18 2013 16:49:26
%S 2,41,109,151,229,251,271,313,337,367,409,439,733,761,971,991,1021,
%T 1031,1069,1289,1297,1303,1429,1471,1489,1759,1783,1789,1811,1871,
%U 1873,1879,2137,2411,2441,2551,2749,2791,2971,3001,3061,3079,3109,3221,3229
%N Primes whose smallest positive primitive root (A001918) is not prime.
%C Subsequence of A222717 = primes whose smallest positive quadratic nonresidue is not a primitive root. (Proof. If p is not in A222717, then the smallest positive quadratic nonresidue of p is a primitive root g. Since the smallest positive quadratic nonresidue is always a prime, g is prime. But since all primitive roots are quadratic nonresidues, g is the smallest positive primitive root of p. Hence p is not in A047936.) - _Jonathan Sondow_, Mar 13 2013.
%H Charles R Greathouse IV, <a href="/A047936/b047936.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%t lst={}; Do[p=Prime[n]; pr=PrimitiveRoot[p]; If[pr>1&&!PrimeQ[pr], AppendTo[lst, p]], {n, 7!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 24 2009 *)
%t Select[Prime[Range[500]],!PrimeQ[PrimitiveRoot[#]]&] (* _Harvey P. Dale_, Oct 24 2011 *)
%o (PARI) select(p->!isprime(lift(znprimroot(p))),primes(999)) \\ reverse order of arguments if using an old version of GP
%o \\ _Charles R Greathouse_ IV, Oct 24 2011
%Y Cf. A222717, A223036.
%K nonn,easy
%O 1,1
%A _Felice Russo_
%E More terms from _James A. Sellers_, Dec 22 1999
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