A050815 Number of positive Fibonacci numbers with n decimal digits.

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

Table of n, a(n) for n=1..105.

Andreas Guthmann, Wieviele k-stellige Fibonaccizahlen gibt es?, Archiv der Mathematik, Vol. 59, No. 4 (1992), pp. 334-340.

Ron Knott, The Fibonacci Numbers.

Ron Knott, Fibonacci Numbers and the Golden Section.

Ron Knott, [Number of digits in Fib(i)] : Calculator.

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.

Cf. A000045, A001622, A002390, A105563, A105565, A060384, A097348.

Sequence in context: A157295 A011485 A084339 * A199791 A199600 A021608

Adjacent sequences: A050812 A050813 A050814 * A050816 A050817 A050818

Keyword

nonn,base

Author

Patrick De Geest, Oct 15 1999

Status

approved