A167379 Let p and q be twin primes, excluding the pair (3,5). Then p+q is always divisible by 6 and we set a(n) = (p+q)/6.

2, 4, 6, 10, 14, 20, 24, 34, 36, 46, 50, 60, 64, 66, 76, 80, 90, 94, 104, 116, 140, 144, 154, 174, 190, 200, 206, 214, 220, 270, 274, 276, 286, 294, 340, 344, 350, 354, 364, 384, 410, 426, 430, 434, 440, 476, 484, 494, 496, 536, 540, 556, 566, 574, 596, 624, 626

Offset

1,1

Comments

By definition, q = p+2. Hence (p+q)/6 = (p+p+2)/6 = (2p+2)/6 = (p+1)/3. Thus a(n) = (1+A001359(n+1))/3. - Jonathan Vos Post, Nov 03 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Formula

a(n) = 2*A002822(n). - R. J. Mathar, Nov 09 2009

a(n) = (1+A001359(n+1))/3. - Jonathan Vos Post, Nov 03 2009

Example

First (lesser of twin prime pair) excluding (3,5) = 5; (5+1)/3 = 2, hence A167379(1) = 2. The 10th (lesser of twin prime pair) excluding (3,5) = 137; (137+1)/3 = 46, hence A167379(10)= 46. - Jonathan Vos Post, Nov 03 2009

Mathematica

Total[#]/6&/@Select[Partition[Prime[Range[3, 500]], 2, 1], #[[2]]-#[[1]] == 2&] (* Harvey P. Dale, Jan 30 2013 *)
2 Select[Range[35000], PrimeQ[6 # - 1] && PrimeQ[6 # + 1] &] (* Vincenzo Librandi, Jun 13 2016 *)

Prog

(Magma) [2*n: n in [1..630] | IsPrime(6*n+1) and IsPrime(6*n-1)]; // Vincenzo Librandi, Jun 13 2016

Crossrefs

Cf. A002822. [Zak Seidov, Nov 02 2009]

Sequence in context: A121386 A007777 A082379 * A213476 A277085 A094589

Adjacent sequences: A167376 A167377 A167378 * A167380 A167381 A167382

Keyword

nonn

Author

Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Nov 02 2009

Extensions

Edited (but not checked) by N. J. A. Sloane, Nov 02 2009

Extended by R. J. Mathar, Nov 09 2009

Status

approved