OFFSET
1,1
COMMENTS
Equivalently, a(n) is the number of Fibonacci numbers < 10^n including F(0) = 0 and F(1) = F(2) = 1 once. - Derek Orr, Jun 01 2014
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Jürgen Spilker, Die Ziffern der Fibonacci-Zahlen, Elemente der Mathematik 58 (Birkhäuser 2003).
Eric Weisstein's World of Mathematics, Fibonacci Number
FORMULA
Limit_{n->oo} a(n)/n = 1/log_10((1+sqrt(5))/2) = 1/A097348 = 4.784... . - Reinhard Zumkeller, Apr 14 2005
EXAMPLE
a(3)=16, as the 16th Fibonacci number is the largest Fibonacci number with 3 digits.
MATHEMATICA
With[{fibs=Fibonacci[Range[300]]}, Flatten[Position[fibs, #]&/@ Table[ Max[ Select[fibs, IntegerLength[#]==n&]], {n, 60}]]] (* Harvey P. Dale, Nov 09 2011 *)
PROG
(Python)
def A072353_list(n):
list = []
x, y, index = 1, 1, 1
while len(list) < n:
if len(str(x)) < len(str(y)):
list.append(index)
x, y = y, x + y
index += 1
return list
print(A072353_list(57)) # M. Eren Kesim, Jul 19 2021
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Shyam Sunder Gupta, Jul 17 2002
EXTENSIONS
More terms from Reinhard Zumkeller, Apr 14 2005
Name edited by Michel Marcus, Jul 19 2021
STATUS
approved