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A192040 Decimal approximation of x such that f(x)=7, where f is the Fibonacci function described in Comments. 1
5, 7, 2, 1, 4, 6, 1, 7, 3, 4, 9, 5, 3, 8, 6, 7, 5, 9, 6, 7, 4, 5, 2, 5, 4, 4, 3, 1, 4, 9, 3, 4, 9, 3, 9, 5, 8, 4, 2, 5, 7, 2, 7, 9, 6, 2, 3, 6, 6, 2, 8, 2, 2, 6, 1, 2, 6, 4, 5, 1, 8, 6, 7, 6, 9, 0, 5, 7, 0, 5, 4, 6, 7, 3, 3, 2, 8, 2, 9, 9, 6, 6, 7, 4, 6, 3, 2, 2, 1, 5, 1, 8, 5, 5, 9, 7, 0, 7, 1, 5 (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

5.721461734953867596745254431493493958425727962366282

MATHEMATICA

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

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

x /. FindRoot[Fibonacci[x] == 7, {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: A196847 A087455 A294403 * A117759 A021640 A155968

Adjacent sequences:  A192037 A192038 A192039 * A192041 A192042 A192043

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jun 21 2011

STATUS

approved

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Last modified October 25 10:46 EDT 2021. Contains 348239 sequences. (Running on oeis4.)