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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153387 Decimal expansion of Sum_{n>=1} 1/Fibonacci(2*n-1). 12
1, 8, 2, 4, 5, 1, 5, 1, 5, 7, 4, 0, 6, 9, 2, 4, 5, 6, 8, 1, 4, 2, 1, 5, 8, 4, 0, 6, 2, 6, 7, 3, 2, 8, 1, 7, 3, 3, 2, 1, 8, 9, 3, 5, 4, 2, 6, 6, 0, 8, 2, 9, 9, 2, 3, 2, 6, 0, 2, 9, 0, 1, 5, 0, 1, 9, 4, 0, 8, 3, 0, 4, 0, 3, 6, 7, 7, 7, 3, 9, 6, 7, 5, 9, 8, 9, 1, 3, 8, 9, 9, 8, 1, 9, 8, 2, 0, 7, 5, 0, 7, 6, 4, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Borwein et al. express the sum in terms of theta functions. - N. J. A. Sloane, May 16 2011

Duverney et al. (1997) proved that this constant is transcendental. - Amiram Eldar, Oct 30 2020

REFERENCES

J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See pp. 202-203.

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..1000

Joerg Arndt, On computing the generalized Lambert series, arXiv:1202.6525v3 [math.CA], (2012).

Daniel Duverney, Keiji Nishioka, Kumiko Nishioka and Iekata Shiokawa, Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 73, No. 7 (1997), pp. 140-142.

FORMULA

Equals sqrt(5)/4 * (T(b^2)^2 - T(b)^2) where T(q) = 1 + 2*sum(n>=1, q^(n^2) ) and b = 1/2*(1-sqrt(5)); see the Arndt reference and the references cited there. - Joerg Arndt, Feb 01 2014

EXAMPLE

1.8245151574069245681...

CROSSREFS

Cf. A079586, A153386, A190649.

Sequence in context: A019775 A274211 A138499 * A342261 A010520 A169847

Adjacent sequences:  A153384 A153385 A153386 * A153388 A153389 A153390

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Dec 25 2008

EXTENSIONS

Definition reconciled to sequence and example by Clark Kimberling, Aug 06 2013

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 December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)