%I #41 Mar 18 2024 12:11:24

%S 4,0,5,4,6,5,1,0,8,1,0,8,1,6,4,3,8,1,9,7,8,0,1,3,1,1,5,4,6,4,3,4,9,1,

%T 3,6,5,7,1,9,9,0,4,2,3,4,6,2,4,9,4,1,9,7,6,1,4,0,1,4,3,2,4,1,4,4,1,0,

%U 0,6,7,1,2,4,8,9,1,4,2,5,1,2,6,7,7,5,2,4,2,7,8,1,7,3,1,3,4,0

%N Decimal expansion of log(3/2).

%D L. B. W. Jolley, Summation of Series, Dover (1961), eq (102), page 20.

%H Harry J. Smith, <a href="/A016578/b016578.txt">Table of n, a(n) for n = 0..20000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Sum {k>=1} 1/(k*3^k). - _Robert G. Wilson v_, Aug 08 2011

%F Equals 1/2 - 1/(2*2^2) + 1/(3*2^3) - 1/(4*2^4) + ... [Jolley].

%F Equals A002391-A002162. - _Michel Marcus_, Sep 17 2016

%F From _Amiram Eldar_, Aug 07 2020: (Start)

%F Equals 2 * arctanh(1/5).

%F Equals Integral_{x=0..oo} 1/(2*exp(x) + 1) dx. (End)

%F log(3/2) = 2*Sum_{n >= 1} 1/(n*P(n, 5)*P(n-1, 5)), where P(n, x) denotes the n-th Legendre polynomial. The first 10 terms of the series gives the approximation log(3/2) = 0.40546510810816438197(04...), correct to 20 decimal places. - _Peter Bala_, Mar 16 2024

%e 0.4054651081081643819780131154643491365719904234624941976140143...

%t RealDigits[Log[3/2],10,111][[1]] (* _Robert G. Wilson v_, Aug 08 2011 *)

%o (PARI) default(realprecision, 20080); x=10*log(3/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b016578.txt", n, " ", d)); \\ _Harry J. Smith_, May 17 2009

%Y Cf. A016529, A002391, A002162.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_