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A167379
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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.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..2000
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FORMULA
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a(n) = 2*A002822(n). - R. J. Mathar, Nov 09 2009
a(n) = (1+A001359(n+1))/3. - Jonathan Vos Post, Nov 03 2009
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(MAGMA) [2*n: n in [1..630] | IsPrime(6*n+1) and IsPrime(6*n-1)]; // Vincenzo Librandi, Jun 13 2016
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CROSSREFS
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Cf. A002822. [Zak Seidov, Nov 02 2009]
Sequence in context: A121386 A007777 A082379 * A213476 A277085 A094589
Adjacent sequences: A167376 A167377 A167378 * A167380 A167381 A167382
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KEYWORD
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nonn
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AUTHOR
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Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Nov 02 2009
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EXTENSIONS
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Edited (but not checked) by N. J. A. Sloane, Nov 02 2009
Extended by R. J. Mathar, Nov 09 2009
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STATUS
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approved
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