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

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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

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

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

Crossrefs

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

Programs

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

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