%I #30 Mar 21 2024 06:19:01
%S 9,1,6,2,9,0,7,3,1,8,7,4,1,5,5,0,6,5,1,8,3,5,2,7,2,1,1,7,6,8,0,1,1,0,
%T 7,1,4,5,0,1,0,1,2,1,9,9,0,8,2,6,2,4,6,7,7,9,1,9,6,7,8,8,1,9,8,0,7,8,
%U 5,3,6,5,7,3,7,9,6,3,0,4,9,0,2,4,2,7,0,5,5,1,0,9,6,7,6,0,9,2
%N Decimal expansion of log(5/2).
%H Harry J. Smith, <a href="/A016579/b016579.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 A016628 minus A002162. - _R. J. Mathar_, Jan 23 2009
%F log(5/2) = 2*Sum_{n >= 1} 1/(n*P(n, 7/3)*P(n-1, 7/3)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(5/2) = 0.916290731874155065183527(19...), correct to 24 decimal places. - _Peter Bala_, Mar 18 2024
%e 0.916290731874155065183527211768011071450101219908262467791967881980785...
%t RealDigits[Log[5/2], 10, 120][[1]] (* _Vincenzo Librandi_, Apr 07 2020 *)
%o (PARI) default(realprecision, 20080); x=10*log(5/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b016579.txt", n, " ", d)); \\ _Harry J. Smith_, May 25 2009
%o (Magma) SetDefaultRealField(RealField(100)); Log(5/2); // _Vincenzo Librandi_, Apr 07 2020
%Y Cf. A016530 (continued fraction).
%K nonn,cons
%O 0,1
%A _N. J. A. Sloane_
%E Leading zero removed and offset adjusted by _R. J. Mathar_, Feb 06 2009