The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 * A264692 A021366 A334366 Adjacent sequences: A259232 A259233 A259234 * A259236 A259237 A259238 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jun 22 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)