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