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A006518 Continued fraction for Sum_{k >= 2} 2^(-Fibonacci(k)).
(Formerly M4677)
4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. J. van der Poorten and Jeffrey Shallit, A specialised continued fraction, Canad. J. Math., 45 (1993), 1067-1079.
G. Xiao, Contfrac
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
Sequence in context: A281400 A283726 A010171 * A094175 A193952 A158508
KEYWORD
nonn,cofr
AUTHOR
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)