A078946 Primes p such that p, p+2, p+6, p+12 and p+14 are consecutive primes.

17, 227, 1277, 1607, 3527, 3917, 4637, 4787, 27737, 38447, 39227, 44267, 71327, 97367, 99707, 113147, 122027, 122387, 124337, 165707, 183497, 187127, 191447, 197957, 198827, 275447, 290657, 312197, 317957, 347057, 349397, 416387, 418337, 421697, 427067, 443867

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Eric Weisstein's World of Mathematics, Prime Triplet.

Formula

a(n) == 17 (mod 30). - Amiram Eldar, Feb 21 2025

Example

227 is in the sequence since 227, 229 = 227 + 2, 233 = 227 + 6, 239 = 227 + 12 and 241 = 227 + 14 are consecutive primes.

Mathematica

Rest@ Select[Prime@ Range@ 36000, AllTrue[{2, 6, 12, 14} + #, PrimeQ] &] (* Michael De Vlieger, Apr 18 2015, Version 10 *)
Select[Partition[Prime[Range[36000]], 5, 1], Differences[#]=={2, 4, 6, 2}&][[All, 1]] (* Harvey P. Dale, Jun 14 2022 *)

Prog

(PARI) isok(p) = isprime(p) && (nextprime(p+1)==p+2) && (nextprime(p+3)== p+6) && (nextprime(p+7)==p+12) && (nextprime(p+13)==p+14); \\ Michel Marcus, Dec 10 2013
(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 21 2025
(Magma) [p: p in PrimesInInterval(7, 1000000) | forall{i: i in [2, 6, 12, 14] | IsPrime(p+i)}]; // Vincenzo Librandi, Apr 19 2015

Crossrefs

Subsequence of A128468.

Subsequence of A078847. - R. J. Mathar, Feb 10 2013

Cf. A001223, A078866, A078867, A078947-A078971, A022006, A022007.

Sequence in context: A296999 A140842 A087608 * A164600 A187636 A152588

Adjacent sequences: A078943 A078944 A078945 * A078947 A078948 A078949

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved