The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A084119 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A084119

Decimal expansion of the Fibonacci binary number, Sum_{k>0} 1/2^F(k), where F(k) = A000045(k).
(history; published version)

#38 by Michel Marcus at Mon Jun 12 02:55:10 EDT 2023

STATUS

reviewed

approved

#37 by Joerg Arndt at Mon Jun 12 01:24:50 EDT 2023

STATUS

proposed

reviewed

#36 by Amiram Eldar at Mon Jun 12 00:42:54 EDT 2023

STATUS

editing

proposed

#35 by Amiram Eldar at Mon Jun 12 00:35:56 EDT 2023

CROSSREFS

Cf. A000045, A010056, A079586, A181313 (continued fraction), A124091 (essentially the same).

#34 by Amiram Eldar at Mon Jun 12 00:28:56 EDT 2023

LINKS

DDavid H. Bailey et al, Jonathan M. Borwein, Richard E., Crandall, and Carl 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.

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

<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

#33 by Amiram Eldar at Mon Jun 12 00:27:05 EDT 2023

MATHEMATICA

RealDigits[N[Sum[1/2^Fibonacci[k], {k, 1, Infinity}], 120]][[1]] (* Amiram Eldar, Jun 12 2023 *)

STATUS

approved

editing

#32 by N. J. A. Sloane at Mon Aug 23 00:43:14 EDT 2021

STATUS

reviewed

approved

#31 by Michel Marcus at Sun Aug 22 05:48:46 EDT 2021

STATUS

proposed

reviewed

#30 by Kevin Ryde at Sun Aug 22 05:34:04 EDT 2021

STATUS

editing

proposed

#29 by Kevin Ryde at Sun Aug 22 05:09:10 EDT 2021

EXAMPLE

1.410278797207865891794043024471063...

CROSSREFS

Cf. A010056, A079586, A006518. See A181313 (continued fraction), A124091 for another version(essentially the same).

STATUS

approved

editing

Discussion

Sun Aug 22

05:11

Kevin Ryde: A181313 is the continued fraction for 1.41027 here, as opposed to A006518 is for 0.91027, ie. 0.5 smaller.