1,1

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)

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

Eric Weisstein's World of Mathematics, Prime Triplet

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

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

Select[Prime[Range[600]], AllTrue[#+{2, 12}, PrimeQ]&] (* Harvey P. Dale, Jun 26 2025 *)

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

Cf. A000040, A001359, A046133, A050266.

Sequence in context: A277718 A067606 A184247 * A331946 A162336 A234346

Adjacent sequences: A046132 A046133 A046134 * A046136 A046137 A046138

nonn,easy

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

approved