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A016627
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Decimal expansion of log(4).
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13
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..20000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Allon G. Percus, Gabriel Istrate, Bruno Goncalves, Robert Z. Sumi and Stefan Boettcher, The Peculiar Phase Structure of Random Graph Bisection, Aug 11, 2008.
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FORMULA
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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->oo} A066066(n)/n. - M. F. Hasler, Oct 20 2013
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EXAMPLE
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1.386294361119890618834464242916353136151000268720510508241360018986787...
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PROG
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(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
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CROSSREFS
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Cf. A016732 (continued fraction).
Sequence in context: A016624 A021263 A081803 * A175184 A019604 A214726
Adjacent sequences: A016624 A016625 A016626 * A016628 A016629 A016630
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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