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!)
A322711 Decimal expansion of the sum of reciprocals of the products of 9 consecutive Fibonacci numbers. 3
4, 5, 7, 1, 5, 2, 2, 7, 6, 2, 0, 6, 4, 8, 1, 8, 3, 7, 2, 5, 9, 8, 4, 4, 5, 5, 7, 2, 8, 8, 9, 5, 1, 8, 5, 4, 9, 1, 1, 3, 7, 2, 6, 0, 1, 2, 5, 5, 7, 9, 3, 8, 1, 5, 8, 9, 6, 0, 7, 5, 1, 7, 8, 7, 0, 5, 4, 0, 1, 1, 3, 3, 3, 7, 6, 6, 7, 8, 6, 3, 4, 2, 1, 2, 1, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-6,1

LINKS

Robert G. Wilson v, Table of n, a(n) for n = -6..10000

Brother Alfred Brousseau, Summation of Infinite Fibonacci Series, The Fibonacci Quarterly, Vol. 7, No. 2 (1969), pp. 143-168. See (23) p. 167.

Stanley Rabinowitz, Algorithmic summation of reciprocals of products of Fibonacci numbers, The Fibonacci Quarterly, Vol. 37 (1999), pp. 122-127, alternative link. See (29) p. 127 or p. 7.

FORMULA

Equals to (319/16380) * (Sum_{k>=1} 1/F(k) - 46816051/13933920), where F(k) is the k-th Fibonacci number.

EXAMPLE

4.57152276206481837259844557288951854911372601255793... * 10^(-7).

MATHEMATICA

digits = 100; f[n_] := Product[Fibonacci[k], {k, n, n+8}]; NSum[1/f[n], {n, 1, Infinity}, WorkingPrecision -> digits, NSumTerms -> digits] // RealDigits[#, 10, digits] & // First (* after Jean-Fran├žois Alcover at A079586 *)

RealDigits[ Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k + 8}], 128], {k, 59}], 10, 111][[1]] (* Robert G. Wilson v, Feb 11 2019 *)

CROSSREFS

Cf. A000045, A079586, A290565.

Sequence in context: A112247 A319260 A237196 * A057055 A177883 A245422

Adjacent sequences:  A322708 A322709 A322710 * A322712 A322713 A322714

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Dec 24 2018

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 June 2 11:35 EDT 2020. Contains 334771 sequences. (Running on oeis4.)