A046135 Primes p such that p+2 and p+12 are primes.

5, 11, 17, 29, 41, 59, 71, 101, 137, 179, 227, 239, 269, 281, 347, 419, 431, 641, 809, 827, 1019, 1049, 1091, 1151, 1277, 1289, 1427, 1481, 1487, 1607, 1697, 1721, 1877, 2027, 2087, 2129, 2141, 2339, 2381, 2687, 2729, 2789, 2999, 3359, 3527, 3581

Offset

1,1

Comments

From Jonathan Vos Post, May 17 2006: (Start)

Could be defined as "Numbers n such that k^3+k^2+n is prime for k = 0, 1, 2."

The following subset is also prime for k = 3: 5, 11, 17, 71, 101, 137, 227, 281, 347, 431, 641, 827, 1151, 1277, 1487. The following subset of those is also prime for k = 4: 17, 71, 101, 227, 827, 1151, 1487. The following subset of those is also prime for k = 5: 827, 1151, 1487. The "17" in A050266's n^3+n^2+17 is because k^3+k^2+17 is prime for k = 1,2,3,4,5,6,7,8,9,10. Between 10000 and 20000 there are 30 members of the k = 0,1,2 sequence, of which these 10 are also prime for k = 3: 10301, 10937, 11057, 11777, 12107, 13997, 15137, 15737, 16061, 19541. The following subset of those is also prime for k = 5: 15137, 15737, 16061. Somewhere in these sequences is a value that breaks the 11-term record of A050266 and indeed any known prime generating polynomial record. (End)

Links

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

Eric Weisstein's World of Mathematics, Prime Triplet

Formula

{n such that n prime, n+2 prime, n+12 prime} = A001359 INTERSECT A046133. - Jonathan Vos Post, May 17 2006

Mathematica

Select[Prime[Range[600]], PrimeQ[# + 2] && PrimeQ[# + 12]&] (* Vincenzo Librandi, Apr 09 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(3600) | IsPrime(p+2) and IsPrime(p+12)]; // Vincenzo Librandi, Apr 09 2013

Crossrefs

Cf. A000040, A001359, A046133, A050266.

Sequence in context: A277718 A067606 A184247 * A331946 A162336 A234346

Adjacent sequences: A046132 A046133 A046134 * A046136 A046137 A046138

Keyword

nonn,easy

Author

Eric W. Weisstein

Extensions

Edited by R. J. Mathar and N. J. A. Sloane, Aug 13 2008

Status

approved