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A005596
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Decimal expansion of Artin's constant product(1-1/(p^2-p), p=prime).
(Formerly M2608)
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27
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3, 7, 3, 9, 5, 5, 8, 1, 3, 6, 1, 9, 2, 0, 2, 2, 8, 8, 0, 5, 4, 7, 2, 8, 0, 5, 4, 3, 4, 6, 4, 1, 6, 4, 1, 5, 1, 1, 1, 6, 2, 9, 2, 4, 8, 6, 0, 6, 1, 5, 0, 0, 4, 2, 0, 9, 4, 7, 4, 2, 8, 0, 2, 4, 1, 7, 3, 5, 0, 1, 8, 2, 0, 4, 0, 0, 2, 8, 0, 8, 2, 3, 4, 4, 3, 0, 4, 3, 1, 7, 0, 8, 7, 2, 5, 0, 5, 6
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OFFSET
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0,1
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REFERENCES
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P. Moree, The formal series Witt transform, Disc. Math., 295 (2005), 143-160. See p. 159.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime constant, Math. Comp., 15 (1961), 396-398.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
H. Cohen, High-precision calculation of Hardy-Littlewood constants, (1998). - From N. J. A. Sloane, Jan 26 2013
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, constant A_1^(1).
Pieter Moree, Artin's primitive root conjecture - a survey, math.NT/0412262
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
G. Niklasch, Artin's constant
_Simon Plouffe_, The Artin's Constant=product(1-1/p**2-p), p=prime)
T. O. Silva, Plouffe's Inverter, The first 500 digits of Artin's constant
Eric Weisstein's World of Mathematics, Artin's constant
Eric Weisstein's World of Mathematics, Full Reptend Prime
Index entries for sequences related to Artin's conjecture
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FORMULA
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Equals product_{j=2..infinity} 1/Zeta(j)^A006206(j), where Zeta(.)=A013661, A002117 etc. is Riemann's zeta function. [From R. J. Mathar, Feb 14 2009]
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EXAMPLE
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0.37395581361920228805472805434641641511162924860615...
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CROSSREFS
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Cf. A048296, A065414, A001913, A001122.
Sequence in context: A131917 A019785 A074176 * A159566 A096385 A205723
Adjacent sequences: A005593 A005594 A005595 * A005597 A005598 A005599
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Tom\'as Oliveira e Silva (http://www.ieeta.pt/~tos)
Fixed my PARI program, had -n Harry J. Smith, May 19 2009
Pari code removed by D. S. McNeil, Dec 26 2010
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STATUS
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approved
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