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URL: https://oeis.org/A045309

⇱ A045309 - OEIS

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A045309
Primes congruent to {0, 2} mod 3.
20
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
1,1
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
Primes p such that 2*p+1 is not a multiple of 3. - Alain Rocchelli, Jan 02 2026
LINKS
FORMULA
a(n) ~ 2n log n. - Charles R Greathouse IV, Apr 20 2015
MATHEMATICA
Select[Prime[Range[150]], MemberQ[{0, 2}, Mod[#, 3]]&] (* Harvey P. Dale, Jun 14 2011 *)
PROG
(Magma) [ p: p in PrimesUpTo(1000) | #[ x: x in ResidueClassRing(p) | x^3 eq 2 ] eq 1 ]; // Klaus Brockhaus, Apr 11 2009
(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
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
Edited by N. J. A. Sloane, Apr 11 2009
STATUS
approved