A262264 - OEIS

%I #26 Sep 15 2022 02:15:08

%S 3,7,23,191,409

%N Primes that are less than the square of their least positive primitive root.

%C Alternatively, primes such that the least positive primitive root is greater than the square root of p.

%C Next term is greater than 10^9.

%D References and links at A001918.

%e The least primitive root of 23 is 5; 5^2 is greater than 23, so 23 is in the sequence.

%e The least primitive root of 409 is 21; 21^2 = 441 is greater than 409, so 409 is in the sequence.

%e 41 is not in the sequence because its least primitive root is 6, and 6^2 < 41.

%t Select[Prime[Range[1000]], PrimitiveRoot[#]^2 > # &]

%o (PARI) /* the following assumes that znprimroot() returns the smallest primitive root */

%o forprime(p=2,10^9,my(g=znprimroot(p));if(lift(g)^2>p,print1(p,", "))); \\ _Joerg Arndt_, Sep 17 2015

%o (Python)

%o from itertools import islice, count

%o from sympy import prime, primitive_root

%o def A262264_gen(): # generator of terms

%o     return filter(lambda p: p < primitive_root(p)**2,(prime(n) for n in count(1)))

%o A262264_list = list(islice(A262264_gen(),5)) # _Chai Wah Wu_, Sep 14 2022

%Y Cf. A001918 (least positive primitive root of n-th prime).

%K nonn,more

%O 1,1

%A _Dale Taylor_, Sep 17 2015