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A068070 Number of digits in 10^n-th Fibonacci number. 3
1, 2, 21, 209, 2090, 20899, 208988, 2089877, 20898764, 208987640, 2089876403, 20898764025, 208987640250, 2089876402500, 20898764024998, 208987640249979, 2089876402499787, 20898764024997874, 208987640249978734 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/10^n tends towards log_10((1+sqrt(5))/2) = 0.2089876402499787337692... - Vladeta Jovovic, Mar 09 2002

LINKS

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Fibonacci Number.

Eric Weisstein's World of Mathematics, Fibonacci Number

Eric Weisstein's World of Mathematics, Lucas Number

FORMULA

Can be calculated easily using the fact that Fibonacci(n) is very close to GoldenRatio^n/(2*GoldenRatio-1) (cf. A000045). - Michael Taktikos, Aug 11 2004

MATHEMATICA

Table[ Floor[ Log[10, Fibonacci[10^n]] + 1], {n, 0, 7} ]

fib10[n_] := Block[{a = N[Log[10, Sqrt[5]/5], 64], b = N[Log[10, (1 + Sqrt[5])/2], 64]}, Floor[a + 10^n*b] + 1]; Table[ fib10[n], {n, 19}] (* Robert G. Wilson v, May 20 2005 *)

FibonacciDigits[n_] := Ceiling[(2*n*ArcCsch[2] - Log[5])/Log[100]]; Table[ FibonacciDigits[10^n], {n, 19}]

CROSSREFS

Cf. A097348.

Sequence in context: A110253 A185634 A077249 * A085953 A225614 A303500

Adjacent sequences:  A068067 A068068 A068069 * A068071 A068072 A068073

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Feb 26 2002

EXTENSIONS

Corrected by Vladeta Jovovic, Sep 01 2004

STATUS

approved

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Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)