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 A005596 Decimal expansion of Artin's constant product(1-1/(p^2-p), p=prime). (Formerly M2608) 48
 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, 8, 9, 8, 1, 6, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harry J. Smith, Table of n, a(n) for n = 0..1000 Ivan Cherednik, A note on Artin's constant, arXiv:0810.2325 [math.NT], 2008. H. Cohen, High-precision calculation of Hardy-Littlewood constants, (1998). 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, arXiv:math/0412262 [math.NT], 204-2012. Pieter Moree, The formal series Witt transform, Discr. Math. 295 (2005), 143-160. See p. 159. 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 R. G. Wilson, V, Letter to N. J. A. Sloane, Aug. 1993 J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime constant, Math. Comp., 15 (1961), 396-398. FORMULA Equals product_{j=2..infinity} 1/Zeta(j)^A006206(j), where Zeta(.)=A013661, A002117 etc. is Riemann's zeta function. - R. J. Mathar, Feb 14 2009 EXAMPLE 0.37395581361920228805472805434641641511162924860615... MATHEMATICA a = Exp[-NSum[ (LucasL[n] - 1)/n PrimeZetaP[n], {n, 2, Infinity}, PrecisionGoal -> 500, WorkingPrecision -> 500, NSumTerms -> 100000]]; RealDigits[a, 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 taken from Mathematica's Help file on PrimeZetaP *) PROG (PARI) prodinf(n=2, 1/zeta(n)^(sumdiv(n, d, moebius(n/d)*(fibonacci(d-1)+fibonacci(d+1)))/n)) \\ Charles R Greathouse IV, Aug 27 2014 CROSSREFS Cf. A048296, A065414, A001913, A001122. Sequence in context: A131917 A019785 A074176 * A159566 A316255 A096385 Adjacent sequences:  A005593 A005594 A005595 * A005597 A005598 A005599 KEYWORD nonn,cons AUTHOR EXTENSIONS More terms from Tomás Oliveira e Silva (http://www.ieeta.pt/~tos) STATUS approved

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Last modified October 19 07:56 EDT 2018. Contains 316337 sequences. (Running on oeis4.)