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

%I A045309 #48 Apr 29 2025 04:53:28
%S A045309 2,3,5,11,17,23,29,41,47,53,59,71,83,89,101,107,113,131,137,149,167,
%T A045309 173,179,191,197,227,233,239,251,257,263,269,281,293,311,317,347,353,
%U A045309 359,383,389,401,419,431,443,449,461,467,479,491,503,509,521,557,563
%N A045309 Primes congruent to {0, 2} mod 3.
%C A045309 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
%C A045309 2, 3 and primes congruent to 5 mod 6. - _Chai Wah Wu_, Apr 28 2025
%H A045309 Vincenzo Librandi, <a href="/A045309/b045309.txt">Table of n, a(n) for n = 1..1000</a>
%F A045309 a(n) ~ 2n log n. - _Charles R Greathouse IV_, Apr 20 2015
%t A045309 Select[Prime[Range[150]],MemberQ[{0,2},Mod[#,3]]&] (* _Harvey P. Dale_, Jun 14 2011 *)
%o A045309 (Magma) [ p: p in PrimesUpTo(1000) | #[ x: x in ResidueClassRing(p) | x^3 eq 2 ] eq 1 ]; // _Klaus Brockhaus_, Apr 11 2009
%o A045309 (PARI) is(n)=isprime(n) && n%3!=1 \\ _Charles R Greathouse IV_, Apr 20 2015
%o A045309 (Python)
%o A045309 from itertools import count, islice
%o A045309 from sympy import isprime
%o A045309 def A045309_gen(): # generator of terms
%o A045309     yield from (2,3)
%o A045309     yield from filter(isprime, count(5,6))
%o A045309 A045309_list = list(islice(A045309_gen(),48)) # _Chai Wah Wu_, Apr 28 2025
%Y A045309 Cf. A040028, A014752, A060121, A003627, A007528, A045410.
%K A045309 nonn,easy
%O A045309 1,1
%A A045309 _N. J. A. Sloane_
%E A045309 Edited by _N. J. A. Sloane_, Apr 11 2009