A072353 a(n) is the index of the largest Fibonacci number containing n digits.

6, 11, 16, 20, 25, 30, 35, 39, 44, 49, 54, 59, 63, 68, 73, 78, 83, 87, 92, 97, 102, 106, 111, 116, 121, 126, 130, 135, 140, 145, 150, 154, 159, 164, 169, 173, 178, 183, 188, 193, 197, 202, 207, 212, 216, 221, 226, 231, 236, 240, 245, 250, 255, 260, 264, 269, 274

Offset

1,1

Comments

Partial sums of A050815: a(n) = Sum_{k=1..n} A050815(k). - Reinhard Zumkeller, Apr 14 2005

Lim_{n->infinity} a(n)/n = 1/log_10((1+sqrt(5))/2) = 4.784... . - Reinhard Zumkeller, Apr 14 2005

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

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

Cf. A072351, A072352, A105564, A105566, A050815, A060384, A000045.

Sequence in context: A118659 A315450 A315451 * A315452 A315453 A315454

Adjacent sequences: A072350 A072351 A072352 * A072354 A072355 A072356

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