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A050815
Number of positive Fibonacci numbers with n decimal digits.
9
6, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5
OFFSET
1,1
COMMENTS
If n>1 then a(n) = 4 or 5. - Robert Gerbicz, Sep 05 2002
The sequence is almost periodic, see also A072353. - Reinhard Zumkeller, Apr 14 2005
LINKS
Andreas Guthmann, Wieviele k-stellige Fibonaccizahlen gibt es?, Archiv der Mathematik, Vol. 59, No. 4 (1992), pp. 334-340.
Jan-Christoph Puchta, The Number of k-Digit Fibonacci Numbers, The Fibonacci Quarterly, Vol. 39, No. 4 (2001), pp. 334-335.
Jürgen Spilker, Die Ziffern der Fibonacci-Zahlen, Elemente der Mathematik, Vol. 58 (Birkhäuser 2003), pp. 26-33.
Eric Weisstein's World of Mathematics, Fibonacci Number.
Eric Weisstein's World of Mathematics, Almost Periodic Function.
FORMULA
Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = log(10)/log(phi) = 1/A097348 = 4.7849719667... - Amiram Eldar, Jan 12 2022
EXAMPLE
At length 1 there are 6 such numbers: 1, 1, 2, 3, 5 and 8.
MATHEMATICA
Drop[Last/@Tally[Table[IntegerLength[Fibonacci[n]], {n, 505}]], -1] (* Jayanta Basu, Jun 01 2013 *)
CROSSREFS
See A098842 for another version.
Sequence in context: A157295 A011485 A084339 * A199791 A199600 A021608
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Oct 15 1999
STATUS
approved