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
Examples
0.5078339228684383921890418407220763742462184334326009...
Links
- Olivier Golinelli, Remote control system of a binary tree of switches - II. balancing for a perfect binary tree, arXiv:2405.16968 [cs.DM], 2024. See p. 4.
- 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.
Programs
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Mathematica
First@ RealDigits[-Derivative[1, 0][PolyLog][0, 1/2], 10, 105] (* Eric W. Weisstein, edited by Michael De Vlieger, Jan 21 2019 *)
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PARI
suminf(n=2,log(n)>>n) \\ Charles R Greathouse IV, Sep 08 2014
Formula
Equals Sum_{n>=2} log(n)/2^n. - Jean-François Alcover, Apr 14 2014
Equals Sum_{n>=1} Lambda(n)/(2^n-1), where Lambda(n) = log(A014963(n)) is the Mangoldt function. - Amiram Eldar, Jul 07 2021
Equals lim_{m->oo} (1/m) * Sum_{k=1..m} f(k), where f(k) = Sum_{primes p <= k, binomial(2*k,k) mod p != 0} 1/p = A334074(k)/A334075(k) (Erdős et al., 1975). - Amiram Eldar, May 25 2025