

A167135


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


7



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
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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+1problem 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



