OFFSET
1,1
REFERENCES
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.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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].
Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 144.
Jean-Paul Delahaye, Premiers jumeaux: frères ennemis? [Twin primes: Enemy Brothers?], Pour la science, No. 260 (Juin 1999), 102-106.
Jean-Claude Evard, Twin primes and their applications. [Cached copy on the Wayback Machine]
Jean-Claude Evard, Twin primes and their applications. [Local cached copy]
Jean-Claude Evard, Twin primes and their applications. [Pdf file of cached 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.
Hayden Tronnolone, A tale of two primes, COLAUMS Space, #3, 2013.
Wikipedia, Twin prime.
FORMULA
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
MATHEMATICA
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 *)
Splice[{#, #+2}]& /@ Select[Prime[Range[PrimePi[619]]], PrimeQ[#+2]&] (* Oliver Seipel, Sep 04 2024 *)
PROG
(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
-- Reinhard Zumkeller, Nov 27 2011
(PARI) p=2; forprime(q=3, 1e3, if(q-p==2, print1(p", "q", ")); p=q) \\ Charles R Greathouse IV, Mar 22 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 03 2002
STATUS
approved