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!)
A192038 Decimal approximation of x such that f(x)=4, where f is the Fibonacci function. 6
4, 5, 4, 9, 1, 1, 2, 5, 5, 6, 5, 0, 7, 7, 4, 3, 2, 3, 9, 2, 0, 3, 2, 2, 5, 0, 3, 9, 6, 9, 0, 2, 9, 6, 7, 7, 7, 9, 7, 7, 7, 5, 1, 5, 7, 1, 2, 1, 2, 5, 5, 3, 0, 9, 7, 8, 5, 2, 9, 4, 1, 0, 1, 2, 5, 6, 2, 6, 3, 8, 4, 8, 1, 7, 4, 2, 5, 6, 4, 3, 0, 8, 4, 6, 0, 0, 4, 9, 4, 5, 2, 0, 9, 7, 4, 1, 6, 9, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..100.

Eric W. Weisstein, MathWorld: Fibonacci Number

FORMULA

f(x) = (phi^x - cos(Pi*x) * phi^(-x))/sqrt(5), where phi = (1+sqrt(5))/2 (the golden ratio). The function f, a generalization over the reals of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3) = 2, f(4) = 3, f(5) = 5. [Corrected by Daniel Forgues, Oct 05 2016]

EXAMPLE

4.549112556507743239203225039690296777977751571212553...

MATHEMATICA

r = GoldenRatio; s = 1/Sqrt[5];

f[x_] := s*(r^x - Cos[Pi*x] * r^(-x));

x /. FindRoot[Fibonacci[x] == 4, {x, 5}, WorkingPrecision -> 100]

RealDigits[%, 10]

(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[

Fibonacci[x], {x, -7, 7}] (* Peter J. C. Moses, Jun 21 2011 *)

PROG

(PARI) phi = (1+sqrt(5))/2; solve(x=4, 5, (phi^x - cos(Pi*x) * phi^(-x))/sqrt(5) - 4) \\ Michel Marcus, Oct 05 2016

CROSSREFS

Cf. A192039, A192040, A192041, A192042, A192043, A192044 (these correspond to f(x) = 6, 7, 1/2, 3/2, phi, phi^2 respectively); A171909, A172081.

Sequence in context: A246954 A045834 A106148 * A046577 A176016 A184833

Adjacent sequences:  A192035 A192036 A192037 * A192039 A192040 A192041

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jun 21 2011

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 October 23 13:55 EDT 2021. Contains 348214 sequences. (Running on oeis4.)