cp's OEIS Frontend

A050815 Number of positive Fibonacci numbers with n decimal digits.

%I A050815 #47 Jul 28 2025 17:18:52
%S A050815 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 A050815 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 A050815 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 A050815 Number of positive Fibonacci numbers with n decimal digits.
%C A050815 If n>1 then a(n) = 4 or 5. - _Robert Gerbicz_, Sep 05 2002
%C A050815 The sequence is almost periodic, see also A072353. - _Reinhard Zumkeller_, Apr 14 2005
%H A050815 Hans J. H. Tuenter, <a href="/A050815/b050815.txt">Table of n, a(n) for n = 1..1001</a>
%H A050815 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 A050815 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html">The Fibonacci Numbers</a>.
%H A050815 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 A050815 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 A050815 Jan-Christoph Puchta, <a href="https://web.archive.org/web/2024*/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 A050815 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 A050815 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>.
%H A050815 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPeriodicFunction.html">Almost Periodic Function</a>.
%F A050815 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
%F A050815 For n>1, a(n) = 4+[{n*alpha+beta}<{alpha}], where alpha=log(10)/log(phi), beta=log(5)/(2*log(phi)), [X] is the Iverson bracket, {x}=x-floor(x), denotes the fractional part of x, and phi=(1+sqrt(5))/2. - _Hans J. H. Tuenter_, Jul 20 2025
%F A050815 a(n) = A072354(n+1)-A072354(n), a first-order difference. - _Hans J. H. Tuenter_, Jul 20 2025
%e A050815 At length 1 there are 6 such numbers: 1, 1, 2, 3, 5 and 8.
%t A050815 Drop[Last/@Tally[Table[IntegerLength[Fibonacci[n]],{n,505}]],-1] (* _Jayanta Basu_, Jun 01 2013 *)
%Y A050815 See A098842 for another version.
%Y A050815 Cf. A000045, A001622, A002390, A072354, A105563, A105565, A060384, A097348.
%K A050815 nonn,base
%O A050815 1,1
%A A050815 _Patrick De Geest_, Oct 15 1999