A072351 Smallest n-digit Fibonacci number.

1, 13, 144, 1597, 10946, 121393, 1346269, 14930352, 102334155, 1134903170, 12586269025, 139583862445, 1548008755920, 10610209857723, 117669030460994, 1304969544928657, 14472334024676221, 160500643816367088, 1100087778366101931, 12200160415121876738

Offset: 1

Author

Shyam Sunder Gupta, Jul 17 2002

Keywords

• base
• nonn

Examples

			a(3)=144, as 144 is smallest 3-digit Fibonacci number.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A072352, A105710, A105712, A105713, A105714, A105715, A105716, A105717, A105718, A105719.

Programs

Maple

F:= proc(n) option remember; local f;
      f:= `if`(n=1, [1$2], F(n-1));
      do f:= [f[2], f[1]+f[2]];
         if length(f[1]) `if`(n=1, 1, F(n-1)[2]):
seq(a(n), n=1..25);  # Alois P. Heinz, Mar 10 2016

Mathematica

a[n_] := Fibonacci[Ceiling[k /. FindRoot[Log[10, Fibonacci[k]] == n-1, {k, 1}]]]; Array[a, 20] (* Jean-François Alcover, Jan 18 2017 *)
With[{fbs=Fibonacci[Range[100]]},Table[SelectFirst[fbs,IntegerLength[#]==n&],{n,20}]] (* Harvey P. Dale, Dec 13 2024 *)

PARI

A072351(n,phi=(sqrt(5)+1)/2)=round(phi^ceil((n*log(10)+log(5)/2)/log(phi))/sqrt(5)) \\  Franklin T. Adams-Watters, May 27 2011

Python

def A072351_list(n):
    list = [1]
    x, y = 1, 1
    while len(list) < n:
        if len(str(x)) < len(str(y)):
            list.append(y)
        x, y = y, x + y
    return list
print(A072351_list(20)) # M. Eren Kesim, Jun 28 2021

Formula

A072351(n) = floor(1/2 + phi^ceiling((n*log(10) + (1/2)*log(5))/log(phi))/sqrt(5)). - Franklin T. Adams-Watters, May 27 2011