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A016650 Decimal expansion of log(27).

%I A016650 #37 Jul 22 2025 07:08:30
%S A016650 3,2,9,5,8,3,6,8,6,6,0,0,4,3,2,9,0,7,4,1,8,5,7,3,5,7,1,0,7,6,7,5,7,7,
%T A016650 1,1,3,9,4,2,4,7,1,6,7,3,4,6,8,2,4,8,3,5,5,2,0,4,0,8,3,0,0,0,9,1,2,4,
%U A016650 8,2,8,7,9,6,5,5,8,2,6,9,0,0,6,2,0,8,4,7,2,6,4,4,4,1,1,9,6,2,6
%N A016650 Decimal expansion of log(27).
%D A016650 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.
%H A016650 Harry J. Smith, <a href="/A016650/b016650.txt">Table of n, a(n) for n = 1..20000</a>
%H A016650 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A016650 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A016650 Log(27) = Integral_{x = 0..oo} sin(4*x)^3/x^2 dx. - _Peter Bala_, Nov 04 2019
%F A016650 From _Peter Bala_, Feb 27 2024: (Start)
%F A016650 Equals 4 - 2*Sum_{k >= 0} 1/((2*k + 1)*(2*k + 3)*4^k).
%F A016650 Continued fraction: 4 - 16/(24 - 96/(84 - 1440/(186 - ... - 16*n*(n + 1)(4*n^2 - 1)/((2*(n + 1)*(10*n + 11)) - ... )))). (End)
%F A016650 Equals 3*A002391. - _R. J. Mathar_, Jul 22 2025
%e A016650 3.295836866004329074185735710767577113942471673468248355204083000912482... - _Harry J. Smith_, May 20 2009
%t A016650 RealDigits[Log[27],10,120][[1]] (* _Harvey P. Dale_, May 07 2012 *)
%o A016650 (PARI) default(realprecision, 20080); x=log(27); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016650.txt", n, " ", d)); \\ _Harry J. Smith_, May 20 2009
%Y A016650 Cf. A016455 (continued fraction).
%K A016650 nonn,cons
%O A016650 1,1
%A A016650 _N. J. A. Sloane_