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A016655 Decimal expansion of log(32) = 5*log(2). 14
3, 4, 6, 5, 7, 3, 5, 9, 0, 2, 7, 9, 9, 7, 2, 6, 5, 4, 7, 0, 8, 6, 1, 6, 0, 6, 0, 7, 2, 9, 0, 8, 8, 2, 8, 4, 0, 3, 7, 7, 5, 0, 0, 6, 7, 1, 8, 0, 1, 2, 7, 6, 2, 7, 0, 6, 0, 3, 4, 0, 0, 0, 4, 7, 4, 6, 6, 9, 6, 8, 1, 0, 9, 8, 4, 8, 4, 7, 3, 5, 7, 8, 0, 2, 9, 3, 1, 6, 6, 3, 4, 9, 8, 2, 0, 9, 3, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Log(32) = 10*log(2)/2 = 5*log(2) = 5*A002162, so 10*(1/2 - 1/4 + 1/6 - 1/8 + 1/10 - 1/2n ...) = log(32). - Eric Desbiaux, Nov 26 2008

-log(2)/2 is the limit for n -> infinity of ((Sum_{k=2..n} arctanh(1/k)) - log(n)). - Jean-Fran├žois Alcover, Aug 07 2014, after Steven Finch

Equals log(sqrt(2)) with offset 0. - Michel Marcus, Feb 19 2017

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].

Steven R. Finch, Errata and Addenda to Mathematical Constants.

Index entries for transcendental numbers

FORMULA

log(2)/2 = (1 - 1/2 - 1/4) + (1/3 - 1/6 - 1/8) + (1/5 - 1/10 - 1/12) + ... [Jolley, Summation of Series, Dover (1961) eq (73)]

Equals (5/4) Sum_{k=1..4} (-1)^(k+1) gamma(0, k/4) where gamma(n,x) denotes the generalized Stieltjes constants. - Peter Luschny, May 16 2018

From Amiram Eldar, Jun 29 2020: (Start)

log(2)/2 = arctanh(1/3) = arcsinh(1/sqrt(8)).

log(2)/2 = Integral_{x=0..Pi/4} tan(x) dx.

log(2)/2 = Sum_{k>=0} (-1)^k/(2*k+2).

log(2)/2 = Sum_{k>=1} 1/A060851(k). (End)

EXAMPLE

3.465735902799726547086160607290882840377500671801276270603400047466968...

MATHEMATICA

RealDigits[5 N [Log[2], 100]] [[1]] (* Vincenzo Librandi, Jan 02 2016 *)

PROG

(PARI) log(32) \\ Charles R Greathouse IV, Jan 24 2012

(MAGMA) [5*Log(2)]; // Vincenzo Librandi, Jan 02 2016

CROSSREFS

Cf. A060851, A195909, A195913, A195697, A016460 (continued fraction).

Sequence in context: A047840 A037189 A083342 * A057757 A332361 A058838

Adjacent sequences:  A016652 A016653 A016654 * A016656 A016657 A016658

KEYWORD

nonn,cons,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 2 02:41 EDT 2020. Contains 335389 sequences. (Running on oeis4.)