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 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 29 02:00 EDT 2022. Contains 354122 sequences. (Running on oeis4.)