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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 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 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. A084119, A124091. - Harry J. Smith, May 04 2009 Sequence in context: A281400 A283726 A010171 * A094175 A193952 A158508 Adjacent sequences:  A006515 A006516 A006517 * A006519 A006520 A006521 KEYWORD nonn,cofr AUTHOR STATUS approved

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)