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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 * A264692 A021366 A334366

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