A068070 Number of digits in 10^n-th Fibonacci number.

1, 2, 21, 209, 2090, 20899, 208988, 2089877, 20898764, 208987640, 2089876403, 20898764025, 208987640250, 2089876402500, 20898764024998, 208987640249979, 2089876402499787, 20898764024997874, 208987640249978734

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, 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,changed

Author

Robert G. Wilson v, Feb 26 2002

Extensions

Corrected by Vladeta Jovovic, Sep 01 2004

Status

approved