A047936 - OEIS

A047936

Primes whose smallest positive primitive root (A001918) is not prime.

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

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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

Index entries for primes by primitive root

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

AUTHOR

Felice Russo

EXTENSIONS

More terms from James A. Sellers, Dec 22 1999

STATUS

approved