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%I M4677 #38 Aug 23 2021 00:42:36
%S 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,
%T 536870655,4,16,3,1,3,7,1,140737488347135,8,128,2,1,1,1,7,2,1,9,1
%N Continued fraction for Sum_{k >= 2} 2^(-Fibonacci(k)).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Harry J. Smith, <a href="/A006518/b006518.txt">Table of n, a(n) for n = 0..564</a>
%H V. Meally, <a href="/A006516/a006516.pdf">Letter to N. J. A. Sloane, May 1975</a>
%H A. J. van der Poorten, <a href="http://www-centre.mpce.mq.edu.au/alfpapers/a107.pdf">Continued fractions of formal power series</a>
%H A. J. van der Poorten and Jeffrey Shallit, <a href="http://dx.doi.org/10.4153/CJM-1993-058-5">A specialised continued fraction</a>, Canad. J. Math., 45 (1993), 1067-1079.
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%F 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
%e 0.91027879720786589179404302... = 0 + 1/(1 + 1/(10 + 1/(6 + 1/(1 + ...)))). - _Harry J. Smith_, May 04 2009
%o (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
%Y Cf. A000045, A084119, A124091, A125600, A181313.
%K nonn,cofr
%O 0,3
%A _N. J. A. Sloane_
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