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} ];
(Magma) [ 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
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Oct 28 2009
STATUS
approved