A006518 Continued fraction for Sum_{k >= 2} 2^(-Fibonacci(k)). (Formerly M4677)

0, 1, 10, 6, 1, 6, 2, 14, 4, 124, 2, 1, 2, 2039, 1, 9, 1, 1, 1, 262111, 2, 8, 1, 1, 1, 3, 1, 536870655, 4, 16, 3, 1, 3, 7, 1, 140737488347135, 8, 128, 2, 1, 1, 1, 7, 2, 1, 9, 1

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Harry J. Smith, Table of n, a(n) for n = 0..564

V. Meally, Letter to N. J. A. Sloane, May 1975

A. J. van der Poorten, Continued fractions of formal power series

A. J. van der Poorten and Jeffrey Shallit, A specialised continued fraction, Canad. J. Math., 45 (1993), 1067-1079.

G. Xiao, Contfrac

Index entries for continued fractions for constants

Formula

Interestingly, a(13)=2^11-2^3-1, a(19)=2^18-2^5-1, a(27)=2^29-2^8-1, a(35)=2^47-2^13-1. - Ralf Stephan, Jun 07 2005

Example

0.91027879720786589179404302... = 0 + 1/(1 + 1/(10 + 1/(6 + 1/(1 + ...)))). - Harry J. Smith, May 04 2009

Prog

(PARI) { allocatemem(932245000); default(realprecision, 10000); x=suminf(k=2, 1/2^fibonacci(k)); c=contfrac(x); for (n=1, 565, write("b006518.txt", n-1, " ", c[n])); } \\ Harry J. Smith, May 04 2009

Crossrefs

Cf. A000045, A084119, A124091, A125600, A181313.

Sequence in context: A283726 A370388 A010171 * A094175 A193952 A158508

Adjacent sequences: A006515 A006516 A006517 * A006519 A006520 A006521

Keyword

nonn,cofr

Author

N. J. A. Sloane

Status

approved