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 A016628 Decimal expansion of log(5). 11
 1, 6, 0, 9, 4, 3, 7, 9, 1, 2, 4, 3, 4, 1, 0, 0, 3, 7, 4, 6, 0, 0, 7, 5, 9, 3, 3, 3, 2, 2, 6, 1, 8, 7, 6, 3, 9, 5, 2, 5, 6, 0, 1, 3, 5, 4, 2, 6, 8, 5, 1, 7, 7, 2, 1, 9, 1, 2, 6, 4, 7, 8, 9, 1, 4, 7, 4, 1, 7, 8, 9, 8, 7, 7, 0, 7, 6, 5, 7, 7, 6, 4, 6, 3, 0, 1, 3, 3, 8, 7, 8, 0, 9, 3, 1, 7, 9, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. Horace S. Uhler, Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17. Proc. Nat. Acad. Sci. U. S. A. 26, (1940). 205-212. 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]. Simon Plouffe, The natural logarithm of 5 to 10000 digits FORMULA From Peter Bala, Nov 11 2019: (Start) log(5) = 2*sqrt(2)*Integral_{t = 0..sqrt(2)/2} (1 - t^2)/(1 + t^4) dt. log(5) = Sum_{n >= 0} (4*n+5)/((4*n+1)*(4*n+3))*(-1/4)^n. log(5) = (1/4)*Sum_{n >= 0} ( 8/(8*n+1) - 4/(8*n+3) - 2/(8*n+5) + 1/(8*n+7) )*(1/16)^n, a BBP-type formula. (End) log(5) = 2*Sum_{n >= 0} (-1)^(n*(n+1)/2)*1/((2*n+1)*2^n). - Peter Bala, Oct 29 2020 log(5) = Integral_{x = 0..1} (x^4 - 1)/log(x) dx. - Peter Bala, Nov 14 2020 EXAMPLE 1.60943791243410037460075933322618763952560135426851772191264789... - Harry J. Smith, May 16 2009 MATHEMATICA RealDigits[Log[5], 10, 125][[1]] (* Alonso del Arte, Oct 04 2014 *) PROG (PARI) default(realprecision, 20080); x=log(5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016628.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009 CROSSREFS Cf. A016733 (continued fraction). - Harry J. Smith, May 16 2009 Sequence in context: A323606 A133077 A200124 * A112246 A189037 A153201 Adjacent sequences:  A016625 A016626 A016627 * A016629 A016630 A016631 KEYWORD nonn,cons,easy AUTHOR STATUS approved

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Last modified January 23 09:55 EST 2021. Contains 340385 sequences. (Running on oeis4.)