A045344 Primes congruent to {1, 2} mod 3.

2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as A045319, except for the 2nd term. - R. J. Mathar, Jan 30 2009

Primes of the form 3*n-+1. - Juri-Stepan Gerasimov, Jan 22 2010

Primes excluding 3. - Juri-Stepan Gerasimov, Apr 20 2010

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

Primes p satisfying the equation gcd(sigma(p-1), p) = 1. - Lechoslaw Ratajczak, Aug 18 2018

Links

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

Crossrefs

Cf. A000040, A045372, A045391.

Programs

Magma

[p: p in PrimesUpTo(740)|p mod 3 in {1,2}] // Vincenzo Librandi, Dec 18 2010

Mathematica

Select[Prime[Range[150]], MemberQ[{1, 2}, Mod[#, 3]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)
Drop[Prime@ Range@ 63, {2}] (* Robert G. Wilson v, Jun 04 2015 *)

PARI

a(n)=if(n<2, 2, prime(n+1)) \\ Charles R Greathouse IV, May 13 2011

Formula

a(n) = A000040(A065475(n)). - Reinhard Zumkeller, Dec 17 2009