A045309 Primes congruent to {0, 2} mod 3.

2, 3, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Also, primes p such that the equation x^3 == y (mod p) has a unique solution x for every choice of y. - Klaus Brockhaus, Mar 02 2001; Michel Drouzy (DrouzyM(AT)noos.fr), Oct 28 2001

2, 3 and primes congruent to 5 mod 6. - Chai Wah Wu, Apr 28 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A040028, A014752, A060121, A003627, A007528, A045410.

Programs

Magma

[ p: p in PrimesUpTo(1000) | #[ x: x in ResidueClassRing(p) | x^3 eq 2 ] eq 1 ]; // Klaus Brockhaus, Apr 11 2009

Mathematica

Select[Prime[Range[150]],MemberQ[{0,2},Mod[#,3]]&] (* Harvey P. Dale, Jun 14 2011 *)

PARI

is(n)=isprime(n) && n%3!=1 \\ Charles R Greathouse IV, Apr 20 2015

Python

from itertools import count, islice
from sympy import isprime
def A045309_gen(): # generator of terms
    yield from (2,3)
    yield from filter(isprime, count(5,6))
A045309_list = list(islice(A045309_gen(),48)) # Chai Wah Wu, Apr 28 2025

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Apr 20 2015

Extensions

Edited by N. J. A. Sloane, Apr 11 2009