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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-François 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. 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, 100]] [] (* 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 STATUS approved

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