A045375 Primes congruent to {1, 2} mod 6.

2, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619, 631, 643, 661, 673, 691

Offset

1,1

Comments

Apart from initial term, same as A002476 = A007645 \ {2} = A045331 \ {2,3}. - M. F. Hasler, Apr 25 2008

Primes of the form 6*m - 3/2 -+ 5/2. A045375 UNION A045410 = A000040. - Juri-Stepan Gerasimov, Jan 28 2010

a(n)^k + 2 is composite for every positive integer k. Proof: For p = a(n) (i.e., p = 2 or p == 1 (mod 3)), p^k + 2 is composite for all k >= 1. If p = 2, then p^k + 2 = 2*(2^(k - 1) + 1) > 2. If p == 1 (mod 3), then p^k == 1 (mod 3), so p^k + 2 == 0 (mod 3) and > 3. - Felix Huber, May 27 2026

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Maple

A045375List := proc(N)
    local i;
    [2, op(select(isprime, [seq(3*i + 1, i = 2 .. floor(N/3))]))];
end proc:
A045375List(691); # Felix Huber, May 27 2026

Mathematica

Select[Prime[Range[150]], MemberQ[{1, 2}, Mod[#, 6]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(740)|p mod 6 in {1, 2}]; // Vincenzo Librandi, Dec 18 2010

Crossrefs

Cf. A002476, A007645, A045331.

Cf. A000040 (the primes), A045410 (the primes of the form 6*k-2-+1). - Juri-Stepan Gerasimov, Jan 28 2010

Sequence in context: A231383 A156012 A106011 * A249419 A331544 A237499

Adjacent sequences: A045372 A045373 A045374 * A045376 A045377 A045378

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 18 2010

Status

approved