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%I #28 Jan 12 2022 08:58:55
%S 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,
%T 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,
%U 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
%N Number of positive Fibonacci numbers with n decimal digits.
%C If n>1 then a(n) = 4 or 5. - _Robert Gerbicz_, Sep 05 2002
%C The sequence is almost periodic, see also A072353. - _Reinhard Zumkeller_, Apr 14 2005
%H Andreas Guthmann, <a href="https://doi.org/10.1007/BF01197048">Wieviele k-stellige Fibonaccizahlen gibt es?</a>, Archiv der Mathematik, Vol. 59, No. 4 (1992), pp. 334-340.
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html">The Fibonacci Numbers</a>.
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html">Fibonacci Numbers and the Golden Section</a>.
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html">[Number of digits in Fib(i)] : Calculator</a>.
%H Jan-Christoph Puchta, <a href="https://www.fq.math.ca/Scanned/39-4/puchta.pdf">The Number of k-Digit Fibonacci Numbers</a>, The Fibonacci Quarterly, Vol. 39, No. 4 (2001), pp. 334-335.
%H Jürgen Spilker, <a href="http://dx.doi.org/10.5169/seals-8480">Die Ziffern der Fibonacci-Zahlen</a>, Elemente der Mathematik, Vol. 58 (Birkhäuser 2003), pp. 26-33.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPeriodicFunction.html">Almost Periodic Function</a>.
%F 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
%e At length 1 there are 6 such numbers: 1, 1, 2, 3, 5 and 8.
%t Drop[Last/@Tally[Table[IntegerLength[Fibonacci[n]],{n,505}]],-1] (* _Jayanta Basu_, Jun 01 2013 *)
%Y See A098842 for another version.
%Y Cf. A000045, A001622, A002390, A105563, A105565, A060384, A097348.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Oct 15 1999
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