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

1,2

Links

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

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

Example

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

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])<length(f[2]) then break fi
      od; f
    end:
a:= n-> `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 *)

Prog

(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

Crossrefs

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

Sequence in context: A164825 A098298 A045725 * A134489 A064525 A065411

Adjacent sequences: A072348 A072349 A072350 * A072352 A072353 A072354

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 17 2002

Status

approved