A259235 Decimal expansion of sqrt(2*sqrt(3*sqrt(4*...))), a variant of Somos's quadratic recurrence constant.

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

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