A181313 Continued fraction expansion of the Fibonacci binary number.

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, 536870655, 1, 2, 1, 15, 1, 3, 3, 1, 1, 1, 2, 140737488347135, 1, 1, 1, 1, 1, 127, 1, 7, 7, 1, 5, 2, 2, 75557863725914321321983, 1, 1, 2, 5, 1, 2047, 2, 2, 5, 1, 31, 6, 1, 1, 3, 2, 2

Offset

0,2

Comments

Essentially the same as A125600. - R. J. Mathar, Oct 14 2010

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..638

D. Bailey, J. Borwein, R. Crandall, and C. Pomerance, On the binary expansions of algebraic numbers, Journal de Théorie des Nombres de Bordeaux 16 (2004), 487-518.

J. H. Loxton and A. van der Poorten, Arithmetic properties of certain functions in several variables III, Bulletin of the Australian Mathematical Society, Volume 16, Issue 01, February 1977, pp 15-47.

J. Shallit and A. van der Poorten, A specialised continued fraction, Can. J. Math. 45 (1993), 1067-79.

Alf van der Poorten, In thrall to Fibonacci

Prog

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

Crossrefs

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

Sequence in context: A127012 A125503 A127009 * A334515 A164089 A300290

Adjacent sequences: A181310 A181311 A181312 * A181314 A181315 A181316

Keyword

cofr,nonn

Author

Charles R Greathouse IV, Oct 12 2010

Extensions

Offset changed by Andrew Howroyd, Aug 09 2024

Status

approved