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A016627 Decimal expansion of log(4). 11
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]

REFERENCES

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.

LINKS

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.

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->oo} A066066(n)/n. - M. F. Hasler, Oct 20 2013

EXAMPLE

1.386294361119890618834464242916353136151000268720510508241360018986787...

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: A016624 A021263 A081803 * A175184 A019604 A214726

Adjacent sequences:  A016624 A016625 A016626 * A016628 A016629 A016630

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 19 14:25 EDT 2014. Contains 240761 sequences.