A174610 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.

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

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

Mathematica

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 *)

Crossrefs

Sequence in context: A196517 A298141 A160210 * A375108 A373924 A028928

Adjacent sequences: A174607 A174608 A174609 * A174611 A174612 A174613

Keyword

cons,nonn

Author

Benoit Cloitre, Mar 23 2010

Status

approved