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 A016627 Decimal expansion of log(4). 22
 1, 3, 8, 6, 2, 9, 4, 3, 6, 1, 1, 1, 9, 8, 9, 0, 6, 1, 8, 8, 3, 4, 4, 6, 4, 2, 4, 2, 9, 1, 6, 3, 5, 3, 1, 3, 6, 1, 5, 1, 0, 0, 0, 2, 6, 8, 7, 2, 0, 5, 1, 0, 5, 0, 8, 2, 4, 1, 3, 6, 0, 0, 1, 8, 9, 8, 6, 7, 8, 7, 2, 4, 3, 9, 3, 9, 3, 8, 9, 4, 3, 1, 2, 1, 1, 7, 2, 6, 6, 5, 3, 9, 9, 2, 8, 3, 7, 3, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Constant cited in the Percus reference. - Jonathan Vos Post, Aug 13 2008 This constant (negated) is also the 1-dimensional analog of Madelung's constant. - Jean-François Alcover, May 20 2014 This constant is the sum over the reciprocals of the hexagonal numbers A000384(n), n >= 1. See the Downey et al. link, and the formula by Robert G. Wilson v below. - Wolfdieter Lang, Sep 12 2016 REFERENCES Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2. LINKS Harry J. Smith, Table of n, a(n) for n = 1..20000 Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Lawrence Downey, Boon W. Ong, and James A. Sellers, Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers, Coll. Math. J., 39, no. 5 (2008), 391-394. Allon G. Percus, Gabriel Istrate, Bruno Goncalves, Robert Z. Sumi and Stefan Boettcher, The Peculiar Phase Structure of Random Graph Bisection, arXiv:0808.1549 [cond-mat.stat-mech], 2008. FORMULA log(4) = sum(k >= 1, H(k)/2^k) where H(k) is the k-th harmonic number. - Benoit Cloitre, Jun 15 2003 Equals 1-sum_{k >= 1} (-1)^k/A002378(k) = 1 + 2*sum_{k >= 0} 1/A069072(k) = 5/4 - sum_{k >= 1} (-1)^k/A007531(k+2). - R. J. Mathar, Jan 23 2009 Equals 2*A002162 = sum_{n >= 1} binomial(2n, n)/(n*4^n) [D. H. Lehmer, Am. Math. Monthly 92 (1985) 449 and Jolley eq. 262]. - R. J. Mathar, Mar 04 2009 log(4) = sum(k >= 1, A191907(4, k)/k ), (conjecture). - Mats Granvik, Jun 19 2011 log(4) = lim_{n -> infinity} A066066(n)/n. - M. F. Hasler, Oct 20 2013 Equals sum_{k >= 1} 1/( 2*k^2 - k ). - Robert G. Wilson v, Aug 31 2014 Equals gamma(0, 1/2) - gamma(0, 1) = -(EulerGamma + polygamma(0, 1/2)), where gamma(n,x) denotes the generalized Stieltjes constants. - Peter Luschny, May 16 2018 EXAMPLE 1.38629436111989061883446424291635313615100026872051050824136... MATHEMATICA RealDigits[Log@ 4, 10, 111][] (* Robert G. Wilson v, Aug 31 2014 *) PROG (PARI) default(realprecision, 20080); x=log(4); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016627.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009, corrected May 19 2009 (PARI) A016627_vec(N)=digits(floor(log(precision(4., N))*10^(N-1))) \\ Or: default(realprecision, N); digits(log(4)\.1^N) \\ M. F. Hasler, Oct 20 2013 CROSSREFS Cf. A016732 (continued fraction). Sequence in context: A021263 A246727 A081803 * A175184 A019604 A214726 Adjacent sequences:  A016624 A016625 A016626 * A016628 A016629 A016630 KEYWORD nonn,cons AUTHOR STATUS approved

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Last modified May 24 19:14 EDT 2020. Contains 334580 sequences. (Running on oeis4.)