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Search: id:A006518
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| A006518 |
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Continued fraction for Sum_{k >= 2} 2^(-Fibonacci(k)).
(Formerly M4677)
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+0
3
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| 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; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. J. van der Poorten and J. O. Shallit, A specialised continued fraction, Canad. J. Math., 45 (1993), 1067-1079.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,564
A. J. van der Poorten, Continued fractions of formal power series
A. J. van der Poorten and J. O. Shallit, A specialised continued fraction, Canad. J. Math., 45 (1993), 1067-1079.
G. Xiao, Contfrac
Index entries for continued fractions for constants
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FORMULA
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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. - R. Stephan, Jun 07 2005
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EXAMPLE
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0.91027879720786589179404302... = 0 + 1/(1 + 1/(10 + 1/(6 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]
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PROGRAM
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(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])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]
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CROSSREFS
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Cf. A084119, A124091. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]
Sequence in context: A038307 A094260 A010171 this_sequence A158508 A102690 A076366
Adjacent sequences: A006515 A006516 A006517 this_sequence A006519 A006520 A006521
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KEYWORD
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nonn,cofr
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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