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

%I A167135 #24 Aug 30 2024 14:31:05
%S A167135 2,3,5,7,11,17,19,23,29,31,41,43,47,53,59,67,71,79,83,89,101,103,107,
%T A167135 113,127,131,137,139,149,151,163,167,173,179,191,197,199,211,223,227,
%U A167135 233,239,251,257,263,269,271,281,283,293,307,311,317,331,347,353,359
%N A167135 Primes congruent to {2, 3, 5, 7, 11} mod 12.
%C A167135 Primes p such that p mod 12 is prime.
%C A167135 Primes of the form 12*n+r where n >= 0 and r is in {2, 3, 5, 7, 11}.
%C A167135 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
%H A167135 Vincenzo Librandi, <a href="/A167135/b167135.txt">Table of n, a(n) for n = 1..1000</a>
%p A167135 isA167135  := n -> isprime(n) and not modp(n, 12) != 1:
%p A167135 select(isA167135, [$1..360]); # _Peter Luschny_, Mar 28 2018
%t A167135 Select[Prime[Range[400]],MemberQ[{2,3, 5, 7, 11},Mod[#,12]]&] (* _Vincenzo Librandi_, Aug 05 2012 *)
%t A167135 Select[Prime[Range[72]], Mod[#, 12] != 1 &] (* _Peter Luschny_, Mar 28 2018 *)
%o A167135 (Magma) [ p: p in PrimesUpTo(760) | p mod 12 in {2, 3, 5, 7, 11} ];
%o A167135 (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) } } ];
%Y A167135 Subsequences: A002145, A007528. Complement: A068228.
%Y A167135 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.
%K A167135 nonn,easy
%O A167135 1,1
%A A167135 _Klaus Brockhaus_, Oct 28 2009