A174610 - OEIS

%I #11 Jul 29 2015 13:49:18

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

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

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

%N Decimal expansion (1/log(Phi))*sum(k>=1,log((2^k*Phi^2+Phi)/(2^k*Phi^2-1)))=2.02197... where Phi=(1+sqrt(5))/2.

%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.

%t digits = 105; $MaxExtraPrecision = digits + 5; NSum[ Log[ (GoldenRatio^2*2^k + GoldenRatio)/(2^k*GoldenRatio^2 - 1)], {k, 1, Infinity}, NSumTerms -> digits, WorkingPrecision -> digits + 5]/Log[GoldenRatio] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Mar 04 2013 *)

%K cons,nonn

%O 1,1

%A _Benoit Cloitre_, Mar 23 2010