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Search: id:A068070
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| A068070 |
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Number of digits in 10^n-th Fibonacci number. |
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+0
4
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| 1, 2, 21, 209, 2090, 20899, 208988, 2089877, 20898764, 208987640, 2089876403, 20898764025, 208987640250, 2089876402500, 20898764024998, 208987640249979, 2089876402499787, 20898764024997874, 208987640249978734
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)/10^n tends towards log[10]((1+sqrt(5))/2) = .2089876402499787337692... - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 09 2002
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LINKS
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Eric Weisstein's World of Mathematics, Fibonacci Number.
Eric Weisstein's World of Mathematics, Fibonacci Number
Eric Weisstein's World of Mathematics, Lucas Number
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FORMULA
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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
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MATHEMATICA
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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}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 20 2005)
FibonacciDigits[n_] := Ceiling[(2*n*ArcCsch[2] - Log[5])/Log[100]]; Table[ FibonacciDigits[10^n], {n, 19}]
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CROSSREFS
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Cf. A097348.
Sequence in context: A037644 A110253 A077249 this_sequence A085953 A037527 A131584
Adjacent sequences: A068067 A068068 A068069 this_sequence A068071 A068072 A068073
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KEYWORD
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nonn,base
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 26 2002
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EXTENSIONS
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Corrected by Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 01 2004
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