A174608 - OEIS

%I #10 May 09 2022 00:47:15

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

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

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

%N Decimal expansion of (1/log(2))*Sum_{k>=0} log(1+1/2^k) = 2.253...

%H Brigitte Vallée, <a href="http://www.numdam.org/item?id=JTNB_2000__12_2_531_0">Digits and continuants in Euclidean algorithms. Ergodic vs tauberian theorems</a>, Journal de théorie des nombres de Bordeaux 12 (2000), 519-558.

%F Equals log(A081845)/A002162. - _R. J. Mathar_, Apr 20 2010

%t digits = 105; 1/Log[2]*NSum[Log[1 + 1/2^k], {k, 0, Infinity}, WorkingPrecision -> digits, NSumTerms -> 70] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 15 2013 *)

%Y Cf. A002162, A081845.

%K cons,nonn

%O 1,1

%A _Benoit Cloitre_, Mar 23 2010