A262264 Primes that are less than the square of their least positive primitive root.

3, 7, 23, 191, 409

Offset: 1

Author

Dale Taylor, Sep 17 2015

Keywords

• nonn
• more

Comments

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

Next term is greater than 10^9.

Examples

			The least primitive root of 23 is 5; 5^2 is greater than 23, so 23 is in the sequence.
The least primitive root of 409 is 21; 21^2 = 441 is greater than 409, so 409 is in the sequence.
41 is not in the sequence because its least primitive root is 6, and 6^2 < 41.
		

References

• References and links at A001918.

Crossrefs

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

Programs

Mathematica

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

PARI

/* the following assumes that znprimroot() returns the smallest primitive root */
forprime(p=2,10^9,my(g=znprimroot(p));if(lift(g)^2>p,print1(p,", "))); \\ Joerg Arndt, Sep 17 2015

Python

from itertools import islice, count
from sympy import prime, primitive_root
def A262264_gen(): # generator of terms
    return filter(lambda p: p < primitive_root(p)**2,(prime(n) for n in count(1)))
A262264_list = list(islice(A262264_gen(),5)) # Chai Wah Wu, Sep 14 2022