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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 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.)