

A046135


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


1



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
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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 11term 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



