A174608 Decimal expansion of (1/log(2))*Sum_{k>=0} log(1+1/2^k) = 2.253...

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, 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, 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

Offset: 1

Author

Benoit Cloitre, Mar 23 2010

Keywords

• cons
• nonn

Links

• Brigitte Vallée, Digits and continuants in Euclidean algorithms. Ergodic vs tauberian theorems, Journal de théorie des nombres de Bordeaux 12 (2000), 519-558.

Crossrefs

Cf. A002162, A081845.

Programs

Mathematica

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 *)

Formula

Equals log(A081845)/A002162. - R. J. Mathar, Apr 20 2010