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 A259235 Decimal expansion of sqrt(2*sqrt(3*sqrt(4*...))), a variant of Somos's quadratic recurrence constant. 2
 2, 7, 6, 1, 2, 0, 6, 8, 4, 1, 9, 5, 7, 4, 9, 8, 0, 3, 3, 2, 3, 0, 4, 5, 4, 6, 4, 6, 5, 8, 0, 1, 3, 1, 1, 0, 4, 8, 7, 6, 1, 2, 5, 9, 8, 0, 7, 1, 5, 3, 0, 4, 8, 5, 0, 9, 5, 0, 7, 4, 5, 9, 6, 1, 3, 7, 5, 5, 9, 5, 5, 9, 1, 9, 4, 3, 9, 2, 7, 1, 5, 8, 3, 4, 8, 0, 1, 7, 2, 6, 6, 3, 0, 8, 9, 8, 9, 4, 4, 3, 4, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 StackExchange, Improving bound on sqrt(2*sqrt(3*sqrt4*...))) Eric Weisstein's MathWorld, Somos's Quadratic Recurrence Constant FORMULA Equals A112302^2. Equals exp( Sum_{n>=1} log(n)/2^(n-1) ). Also equals exp(-2*PolyLog'(0,1/2)), where PolyLog' is the derivative of PolyLog(n,x) w.r.t. n. EXAMPLE 2.7612068419574980332304546465801311048761259807153... MATHEMATICA RealDigits[Exp[-2*Derivative[1, 0][PolyLog][0, 1/2]], 10, 102] // First RealDigits[Exp[2*Sum[(1/2)^n*Log[n], {n, 2, 2000}]], 10, 100][[1]] (* G. C. Greubel, Sep 30 2018 *) PROG (PARI) exp(sumpos(n=1, log(n+1)/2^n)) \\ Charles R Greathouse IV, Apr 18 2016 (Magma) SetDefaultRealField(RealField(100)); Exp(2*(&+[(1/2)^n*Log(n): n in [2..2000]])); // G. C. Greubel, Sep 30 2018 CROSSREFS Cf. A112302, A114124. Sequence in context: A193746 A070524 A259830 * A371801 A264692 A021366 Adjacent sequences: A259232 A259233 A259234 * A259236 A259237 A259238 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jun 22 2015 STATUS approved

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Last modified September 9 01:17 EDT 2024. Contains 375759 sequences. (Running on oeis4.)