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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
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
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 February 24 17:05 EST 2024. Contains 370307 sequences. (Running on oeis4.)