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A077800
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List of twin primes {p, p+2}.
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105
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3, 5, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 239, 241, 269, 271, 281, 283, 311, 313, 347, 349, 419, 421, 431, 433, 461, 463, 521, 523, 569, 571, 599, 601, 617, 619
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Dave Platt and Tim Trudgian, Improved bounds on Brun's constant, in: David H. Bailey et al. (eds), From Analysis to Visualization, JBCC 2017, Springer Proceedings in Mathematics & Statistics, Vol 313, Springer, Cham, 2020, preprint, arXiv:1803.01925 [math.NT], 2018.
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FORMULA
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Sum_{n>=1} 1/a(n) is in the interval (1.840503, 2.288490) (Platt and Trudgian, 2020). The conjectured value based on assumptions about the distribution of twin primes is A065421. - Amiram Eldar, Oct 15 2020
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MATHEMATICA
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Sort[ Join[ Select[ Prime[ Range[ 115]], PrimeQ[ # - 2] &], Select[ Prime[ Range[ 115]], PrimeQ[ # + 2] &]]] (* Robert G. Wilson v, Jun 09 2005 *)
Select[ Partition[ Prime@ Range@ 115, 2, 1], #[[1]] + 2 == #[[2]] &] // Flatten
Flatten[Select[{#, # + 2} & /@Prime[Range[1000]], PrimeQ[Last[#]]&]] (* Vincenzo Librandi, Nov 01 2012 *)
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PROG
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(Haskell)
a077800 n = a077800_list !! (n-1)
a077800_list = concat $ zipWith (\p q -> if p == q+2 then [q, p] else [])
(tail a000040_list) a000040_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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