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 A047936 Primes whose smallest positive primitive root (A001918) is not prime. 4
 2, 41, 109, 151, 229, 251, 271, 313, 337, 367, 409, 439, 733, 761, 971, 991, 1021, 1031, 1069, 1289, 1297, 1303, 1429, 1471, 1489, 1759, 1783, 1789, 1811, 1871, 1873, 1879, 2137, 2411, 2441, 2551, 2749, 2791, 2971, 3001, 3061, 3079, 3109, 3221, 3229 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 MATHEMATICA 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 *) Select[Prime[Range[500]], !PrimeQ[PrimitiveRoot[#]]&] (* Harvey P. Dale, Oct 24 2011 *) PROG (PARI) select(p->!isprime(lift(znprimroot(p))), primes(999)) \\ reverse order of arguments if using an old version of GP \\ _Charles R Greathouse_ IV, Oct 24 2011 CROSSREFS Cf. A222717, A223036. Sequence in context: A073468 A073186 A103335 * A007533 A088565 A090195 Adjacent sequences:  A047933 A047934 A047935 * A047937 A047938 A047939 KEYWORD nonn,easy,changed AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 22 1999 STATUS approved

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