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 A072112 Decimal expansion of Hall and Tenenbaum constant. 3
 3, 2, 8, 6, 7, 4, 1, 6, 2, 9, 0, 8, 5, 4, 6, 2, 1, 6, 8, 1, 8, 2, 8, 4, 5, 1, 4, 0, 4, 3, 1, 1, 5, 1, 1, 8, 9, 7, 6, 9, 4, 1, 5, 4, 7, 6, 5, 5, 7, 8, 1, 9, 0, 9, 6, 1, 5, 5, 1, 3, 3, 2, 3, 9, 0, 9, 5, 7, 0, 5, 1, 5, 9, 6, 9, 6, 5, 7, 1, 2, 5, 5, 0, 2, 2, 1, 8, 2, 2, 6, 1, 8, 9, 1, 5, 6, 8, 8, 9, 3, 1, 9, 1, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For any multiplicative function g with values -1<= g(k) <= 1, for any real x >=2, Sum( i<= x, g(i) ) << x * exp{ -K * Sum( p<=x, (1-g(p))/p ) } and K is the optimal constant satisfying this inequality (Hall and Tenenbaum, 1991). Named after the British mathematician Richard Roxby Hall and the French mathematician Gérald Tenenbaum (b. 1952). - Amiram Eldar, Jun 22 2021 REFERENCES G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, p. 348, Publications de l'Institut Cartan, 1990. LINKS Table of n, a(n) for n=0..103. R. R. Hall and G. Tenenbaum, Effective mean value estimates for complex multiplicative functions, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 110, No. 2 (1991), pp. 337-351. FORMULA K = cos(S) = 0.3286... where S is the root 0 < S < 2*Pi of sin(S)+(Pi-S)*cos(S) = Pi/2. EXAMPLE 0.32867416290854621681828451404311511897694154765578... MATHEMATICA digits = 104; x /. FindRoot[Pi*x + Sqrt[1 - x^2] - x*ArcCos[x] == Pi/2, {x, 0}, WorkingPrecision -> digits] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 15 2013 *) PROG (PARI) \p 200; cos(solve(X=0, 2*Pi, sin(X)+(Pi-X)*cos(X)-Pi/2)) CROSSREFS Cf. A072113. Sequence in context: A072657 A098163 A260323 * A071658 A089860 A130960 Adjacent sequences: A072109 A072110 A072111 * A072113 A072114 A072115 KEYWORD cons,easy,nonn AUTHOR Benoit Cloitre, Jun 19 2002 STATUS approved

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Last modified September 27 17:53 EDT 2023. Contains 365714 sequences. (Running on oeis4.)