|
|
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
|
|
|
MATHEMATICA
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|