The On-Line Encyclopedia of Integer Sequences (OEIS)

A167119 revision #7

A167119

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

2, 3, 5, 7, 11, 29, 31, 37, 41, 59, 67, 83, 89, 107, 109, 137, 163, 167, 193, 197, 211, 223, 239, 241, 263, 271, 293, 317, 349, 353, 367, 379, 397, 401, 419, 421, 431, 449, 457, 479, 499, 509, 523, 557, 577, 587, 601, 613, 631, 653, 661, 683, 691, 709, 733, 739, 743, 757

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OFFSET

1,1

COMMENTS

Primes which have a remainder mod 13 that is prime.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

Union of A141858, A100202, A102732, A140371 and A140373. [R. J. Mathar, Oct 29 2009]

EXAMPLE

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

MATHEMATICA

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

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

PROG

(PARI) {forprime(p=2, 740, if(isprime(p%13), print1(p, ", ")))} [From Klaus Brockhaus, Oct 28 2009]

(MAGMA) [ p: p in PrimesUpTo(740) | p mod 13 in {2, 3, 5, 7, 11} ]; [From Klaus Brockhaus, Oct 28 2009]

CROSSREFS

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.

Sequence in context: A373044 A036342 A114421 * A165682 A296924 A343423

Adjacent sequences: A167116 A167117 A167118 * A167120 A167121 A167122

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Oct 27 2009

EXTENSIONS

Edited by Klaus Brockhaus and R. J. Mathar, Oct 28 2009 and Oct 29 2009

STATUS

proposed