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

3, 7, 23, 191, 409

Offset

1,1

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.

References

References and links at A001918.

Links

Table of n, a(n) for n=1..5.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A048721 A113824 A121883 * A060235 A343815 A090188

Adjacent sequences: A262261 A262262 A262263 * A262265 A262266 A262267

Keyword

nonn,more

Author

Dale Taylor, Sep 17 2015

Status

approved