A167135 Primes congruent to {2, 3, 5, 7, 11} mod 12.

2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 67, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 191, 197, 199, 211, 223, 227, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 317, 331, 347, 353, 359

Offset

1,1

Comments

Primes p such that p mod 12 is prime.

Primes of the form 12*n+r where n >= 0 and r is in {2, 3, 5, 7, 11}.

Except for the prime 2, these are the primes that are encountered in the set of numbers {x, f(f(x))} where x is of the form 4k+3 with k>=0, and where f(x) is the 3x+1-problem function, and f(f(x)) the second iteration value. Indeed this sequence is the set union of 2 and A002145 (4k+3 primes) and A007528 (6k+5 primes), since f(f(4k+3))=6k+5. Equivalently one does not get any prime from A068228 (the complement of the present sequence). - Michel Marcus and Bill McEachen, May 07 2016

Links

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

Maple

isA167135  := n -> isprime(n) and not modp(n, 12) != 1:
select(isA167135, [$1..360]); # Peter Luschny, Mar 28 2018

Mathematica

Select[Prime[Range[400]], MemberQ[{2, 3, 5, 7, 11}, Mod[#, 12]]&] (* Vincenzo Librandi, Aug 05 2012 *)
Select[Prime[Range[72]], Mod[#, 12] != 1 &] (* Peter Luschny, Mar 28 2018 *)

Prog

(Magma) [ p: p in PrimesUpTo(760) | p mod 12 in {2, 3, 5, 7, 11} ]; (* or *)
[ p: p in PrimesUpTo(760) | exists(t){ n: n in [0..p div 12] | exists(u){ r: r in {2, 3, 5, 7, 11} | p eq (12*n+r) } } ];

Crossrefs

Subsequences: A002145, A007528. Complement: A068228.

Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135, A167119: primes p such that p mod k is prime, for k = 3..13 resp.

Sequence in context: A074647 A108543 A042988 * A129990 A301590 A293194

Adjacent sequences: A167132 A167133 A167134 * A167136 A167137 A167138

Keyword

nonn,easy

Author

Klaus Brockhaus, Oct 28 2009

Status

approved