A181313 - OEIS

%I #23 Aug 09 2024 15:11:29

%S 1,2,2,3,2,28,1,13,1,2,1,123,1,6,1,2039,2,2,6,262111,1,35,1,1,3,

%T 536870655,1,2,1,15,1,3,3,1,1,1,2,140737488347135,1,1,1,1,1,127,1,7,7,

%U 1,5,2,2,75557863725914321321983,1,1,2,5,1,2047,2,2,5,1,31,6,1,1,3,2,2

%N Continued fraction expansion of the Fibonacci binary number.

%C Essentially the same as A125600. - _R. J. Mathar_, Oct 14 2010

%H Charles R Greathouse IV, <a href="/A181313/b181313.txt">Table of n, a(n) for n = 0..638</a>

%H D. Bailey, J. Borwein, R. Crandall, and C. Pomerance, <a href="https://doi.org/10.5802/jtnb.457">On the binary expansions of algebraic numbers</a>, Journal de Théorie des Nombres de Bordeaux 16 (2004), 487-518.

%H J. H. Loxton and A. van der Poorten, <a href="http://dx.doi.org/10.1017/S0004972700022978">Arithmetic properties of certain functions in several variables III</a>, Bulletin of the Australian Mathematical Society, Volume 16, Issue 01, February 1977, pp 15-47.

%H J. Shallit and A. van der Poorten, <a href="http://dx.doi.org/10.4153/CJM-1993-058-5">A specialised continued fraction</a>, Can. J. Math. 45 (1993), 1067-79.

%H Alf van der Poorten, <a href="http://www.maths.mq.edu.au/~alf/_Thrall.pdf">In thrall to Fibonacci</a>

%o (PARI) contfrac(suminf(n=1,2.^-fibonacci(n)))

%Y Cf. A084119 (decimal expansion), A125600 (essentially the same), A006518.

%K cofr,nonn

%O 0,2

%A _Charles R Greathouse IV_, Oct 12 2010

%E Offset changed by _Andrew Howroyd_, Aug 09 2024