A098842 -id:A098842 - cp's OEIS frontend

A261812 First differences of A098842.

-2, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0

Offset: 1

Andrew R. Reiter, Sep 01 2015

Most@ Differences[ Last /@ Tally[ Max[ IntegerLength@#, 1] & /@ Fibonacci[ Range[0, 900]]]] (* Giovanni Resta, Sep 02 2015 *)

import sys
import math
F = [F0,F1] = [0,1]
c = 2
c0 = 0
ll0 = 1
while True:
        T = F[0] + F[1]
        F[0] = F[1]
        F[1] = T
        dfn = 1 + math.log10(T)
        ll = math.floor(dfn)
        if ll0 != ll:
                if c0 != 0:
                        sys.stdout.write("%d," % (c-c0))
                ll0 = ll
                c0 = c
                c = 1
                continue
        c += 1

a(n) = A098842(n+1) - A098842(n).

A050815 Number of positive Fibonacci numbers with n decimal digits.

Original entry on oeis.org

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

Patrick De Geest, Oct 15 1999

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

			At length 1 there are 6 such numbers: 1, 1, 2, 3, 5 and 8.

Hans J. H. Tuenter, Table of n, a(n) for n = 1..1001
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.

See A098842 for another version.

Cf. A000045, A001622, A002390, A072354, A105563, A105565, A060384, A097348.

Drop[Last/@Tally[Table[IntegerLength[Fibonacci[n]],{n,505}]],-1] (* Jayanta Basu, Jun 01 2013 *)

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
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
a(n) = A072354(n+1)-A072354(n), a first-order difference. - Hans J. H. Tuenter, Jul 20 2025

A117768 Number of Lucas numbers with n digits.

Original entry on oeis.org

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: 0

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Cf. A000204. Same as A050815 and A098842 but without the first 3 numbers.

cp's OEIS Frontend

A261812 First differences of A098842.

Views

Author

Keywords

Programs

Mathematica

Python

Formula

A050815 Number of positive Fibonacci numbers with n decimal digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A117768 Number of Lucas numbers with n digits.

Views

Author

Keywords

Crossrefs