%I #49 Sep 08 2022 08:44:55
%S 2,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
%T 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,
%U 191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307
%N Primes congruent to {1, 2} mod 3.
%C Same as A045319, except for the 2nd term. - _R. J. Mathar_, Jan 30 2009
%C Primes of the form 3*n-+1. - _Juri-Stepan Gerasimov_, Jan 22 2010
%C Primes excluding 3. - _Juri-Stepan Gerasimov_, Apr 20 2010
%C Primes p such that p^2 + 2 is composite. 3 is the only prime p such that p^2 + 2 (= 11) is prime. All numbers p^2 + 2 for primes p = 2 and p > 3 are divisible by 3. - _Jaroslav Krizek_, Nov 25 2013
%C Primes p satisfying the equation gcd(sigma(p-1), p) = 1. - _Lechoslaw Ratajczak_, Aug 18 2018
%H Vincenzo Librandi, <a href="/A045344/b045344.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000040(A065475(n)). - _Reinhard Zumkeller_, Dec 17 2009
%t Select[Prime[Range[150]], MemberQ[{1, 2}, Mod[#, 3]] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2012 *)
%t Drop[Prime@ Range@ 63, {2}] (* _Robert G. Wilson v_, Jun 04 2015 *)
%o (Magma) [p: p in PrimesUpTo(740)|p mod 3 in {1,2}] // _Vincenzo Librandi_, Dec 18 2010
%o (PARI) a(n)=if(n<2, 2, prime(n+1)) \\ _Charles R Greathouse IV_, May 13 2011
%Y Cf. A000040, A045372, A045391.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_