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A192039 Decimal approximation of x such that f(x)=6, where f is the Fibonacci function described in Comments. 1
5, 3, 9, 1, 8, 4, 9, 6, 0, 6, 9, 0, 1, 7, 7, 5, 5, 2, 1, 2, 8, 0, 4, 0, 8, 4, 4, 2, 0, 8, 3, 4, 7, 9, 7, 9, 9, 4, 7, 8, 8, 2, 9, 1, 4, 3, 1, 4, 0, 1, 3, 1, 5, 4, 6, 1, 7, 4, 8, 8, 4, 9, 8, 6, 2, 7, 3, 6, 3, 1, 8, 8, 4, 9, 3, 1, 9, 9, 0, 9, 7, 2, 6, 0, 8, 6, 8, 1, 5, 8, 8, 5, 9, 1, 4, 0, 4, 1, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

f(x)=(r^x-r^(-x*cos[Pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2.  This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

LINKS

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

EXAMPLE

5.391849606901775521280408442083479799478829143140

MATHEMATICA

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

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

x /. FindRoot[Fibonacci[x] == 6, {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 *)

CROSSREFS

Cf. A192038.

Sequence in context: A078302 A199438 A220129 * A305327 A112812 A241624

Adjacent sequences:  A192036 A192037 A192038 * A192040 A192041 A192042

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jun 21 2011

STATUS

approved

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Last modified September 24 14:16 EDT 2021. Contains 347643 sequences. (Running on oeis4.)