A174609 Decimal expansion 2+(1/log(Phi))*sum(k>=3,log(((2^k-1)*Phi^2+2*Phi)/((2^k-1)*Phi^2-2)))=3.1152... where Phi=(1+sqrt(5))/2.

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

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 - 1) + 2*GoldenRatio)/((2^k - 1)*GoldenRatio^2 - 2)], {k, 3, Infinity}, NSumTerms -> digits, WorkingPrecision -> digits + 5]/Log[GoldenRatio] + 2 // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 04 2013 *)

Crossrefs

Sequence in context: A320436 A135228 A021325 * A280533 A229288 A181109

Adjacent sequences: A174606 A174607 A174608 * A174610 A174611 A174612

Keyword

cons,nonn

Author

Benoit Cloitre, Mar 23 2010

Status

approved