%I #14 Sep 08 2022 08:45:48

%S 2,3,5,7,11,29,31,37,41,59,67,83,89,107,109,137,163,167,193,197,211,

%T 223,239,241,263,271,293,317,349,353,367,379,397,401,419,421,431,449,

%U 457,479,499,509,523,557,577,587,601,613,631,653,661,683,691,709,733,739,743,757

%N Primes congruent to 2, 3, 5, 7 or 11 (mod 13).

%C Primes which have a remainder mod 13 that is prime.

%C Union of A141858, A100202, A102732, A140371 and A140373. - _R. J. Mathar_, Oct 29 2009

%H Vincenzo Librandi, <a href="/A167119/b167119.txt">Table of n, a(n) for n = 1..1000</a>

%e 11 mod 13 = 11, 29 mod 13 = 3, 31 mod 13 = 5, hence 11, 29 and 31 are in the sequence.

%t f[n_]:=PrimeQ[Mod[n,13]]; lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,6,6!}];lst

%t Select[Prime[Range[4000]],MemberQ[{2, 3, 5, 7, 11},Mod[#,13]]&] (* _Vincenzo Librandi_, Aug 05 2012 *)

%o (PARI) {forprime(p=2, 740, if(isprime(p%13), print1(p, ",")))} \\ _Klaus Brockhaus_, Oct 28 2009

%o (Magma) [ p: p in PrimesUpTo(740) | p mod 13 in {2, 3, 5, 7, 11} ]; // _Klaus Brockhaus_, Oct 28 2009

%Y Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135: primes p such that p mod k is prime, for k = 3..12 resp.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009

%E Edited by _Klaus Brockhaus_ and _R. J. Mathar_, Oct 28 2009 and Oct 29 2009