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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 30 05:55 EST 2023. Contains 359939 sequences. (Running on oeis4.)