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

Author

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

Keywords

• nonn

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

Examples

			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
		

Links

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

Crossrefs

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

Programs

Magma

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

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 *)

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

Extensions

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

Extended by R. J. Mathar, Nov 09 2009