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A072351 Smallest n-digit Fibonacci numbers. 12
1, 13, 144, 1597, 10946, 121393, 1346269, 14930352, 102334155, 1134903170, 12586269025, 139583862445, 1548008755920, 10610209857723, 117669030460994, 1304969544928657, 14472334024676221, 160500643816367088, 1100087778366101931, 12200160415121876738 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

A072351(n)=floor(.5+phi^ceil((n*log(10)+.5*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-Fran├žois Alcover, Jan 18 2017 *)

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

CROSSREFS

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

Sequence in context: A234601 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

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Last modified March 23 21:31 EDT 2017. Contains 283985 sequences.