A114124 Decimal expansion of logarithm of A112302.

5, 0, 7, 8, 3, 3, 9, 2, 2, 8, 6, 8, 4, 3, 8, 3, 9, 2, 1, 8, 9, 0, 4, 1, 8, 4, 0, 7, 2, 2, 0, 7, 6, 3, 7, 4, 2, 4, 6, 2, 1, 8, 4, 3, 3, 4, 3, 2, 6, 0, 0, 9, 2, 9, 5, 3, 6, 6, 3, 9, 2, 7, 5, 0, 3, 5, 1, 5, 2, 2, 5, 8, 0, 8, 9, 7, 1, 0, 8, 6, 1, 8, 3, 6, 9, 0, 1, 5, 3, 8, 5, 5, 3, 5, 4, 4, 0, 7, 5, 4, 1, 8, 8, 8, 3

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Dawei Lu and Zexi Song, Some new continued fraction estimates of the Somos' quadratic recurrence constant, Journal of Number Theory, Volume 155, October 2015, Pages 36-45.

Dawei Lu, Xiaoguang Wang, and Ruiqing Xu, Some New Exponential-Function Estimates of the Somos' Quadratic Recurrence Constant, Results in Mathematics (2019) Vol. 74, No. 1, 6.

Paul Erdős, Ronald L. Graham, Imre Z. Ruzsa and Ernst G. Straus, On the prime factors of C(2n, n), Mathematics of Computation, Vol. 29, No. 129 (1975), pp. 83-92.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 183.

Yusuke Kobayashi and Ryoga Mahara, Approximation algorithm for Steiner tree problem with neighbor-induced cost, J. Operations Res. Soc. Japan, (2023) Vol. 66, No. 1, 18-36. See p. 32.

Jörg Neunhäuserer, On the universality of Somos' constant, arXiv:2006.02882 [math.DS], 2020.

Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant

Xu You and Di-Rong Chen, Improved continued fraction sequence convergent to the Somos' quadratic recurrence constant, Mathematical Analysis and Applications, Volume 436, Issue 1, 1 April 2016, Pages 513-520.

Formula

Sum_{n>=2} log(n)/2^n. - Jean-François Alcover, Apr 14 2014

Equals Lim_{k -> infinity} (1/k) Sum_{i=1..k} A334074(i)/A334075(i). - Amiram Eldar, Apr 14 2020

Equals Sum_{n>=1} Lambda(n)/(2^n-1), where Lambda(n) = log(A014963(n)) is the Mangoldt function. - Amiram Eldar, Jul 07 2021

Example

0.507833922...

Mathematica

First@ RealDigits[-Derivative[1, 0][PolyLog][0, 1/2], 10, 105] (* Eric W. Weisstein, edited by Michael De Vlieger, Jan 21 2019 *)

Prog

(PARI) suminf(n=2, log(n)>>n) \\ Charles R Greathouse IV, Sep 08 2014

Crossrefs

Cf. A014963, A112302, A334074, A334075.

Sequence in context: A190147 A346190 A108745 * A155827 A244045 A084248

Adjacent sequences: A114121 A114122 A114123 * A114125 A114126 A114127

Keyword

nonn,cons

Author

Eric W. Weisstein, Feb 08 2006

Status

approved