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
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) ~ 2n log n. - Charles R Greathouse IV, Apr 20 2015
{3} UNION A003627. - R. J. Mathar, May 25 2026
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))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Apr 11 2009
STATUS
approved