login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A338305 Decimal expansion of Sum_{k>=0} 1/F(2^k+1), where F(k) is the k-th Fibonacci number (A000045). 2
1, 7, 3, 0, 0, 3, 8, 2, 2, 2, 5, 0, 4, 2, 4, 3, 2, 4, 2, 3, 0, 4, 1, 2, 3, 5, 6, 6, 4, 9, 6, 8, 9, 9, 0, 1, 0, 3, 4, 7, 9, 5, 5, 0, 0, 4, 8, 1, 0, 3, 0, 9, 4, 1, 5, 5, 5, 6, 7, 0, 8, 7, 7, 7, 5, 5, 8, 0, 1, 1, 6, 0, 8, 0, 9, 7, 2, 2, 6, 0, 4, 5, 3, 7, 3, 7, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Erdős and Graham (1980) asked whether this constant is irrational or transcendental.

Badea (1987) proved that it is irrational.

Becker and Töpper (1994) proved that it is transcendental.

Note that a similar sum, Sum_{k>=0} 1/F(2^k) = (7-sqrt(5))/2 (A079585), is quadratic rational in Q(sqrt(5)).

LINKS

Table of n, a(n) for n=1..87.

Catalin Badea, The irrationality of certain infinite series, Glasgow Mathematical Journal, Vol. 29, No. 2 (1987), pp. 221-228.

Paul-Georg Becker and Thomas Töpper, Transcendency results for sums of reciprocals of linear recurrences, Mathematische Nachrichten, Vol. 168, No. 1 (1994), pp. 5-17.

Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980, p. 64-65.

FORMULA

Equals Sum_{k>=0} 1/A192222(k).

EXAMPLE

1.73003822250424324230412356649689901034795500481030...

MATHEMATICA

RealDigits[Sum[1/Fibonacci[2^n + 1], {n, 0, 10}], 10, 100][[1]]

PROG

(PARI) suminf(k=0, 1/fibonacci(2^k+1)) \\ Michel Marcus, Oct 21 2020

CROSSREFS

Cf. A000045, A079585, A192222, A338304.

Sequence in context: A038268 A100983 A103237 * A239120 A021582 A098459

Adjacent sequences:  A338302 A338303 A338304 * A338306 A338307 A338308

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Oct 21 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)