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A072351 Smallest n-digit Fibonacci number.

%I A072351 #33 Dec 13 2024 17:52:18
%S A072351 1,13,144,1597,10946,121393,1346269,14930352,102334155,1134903170,
%T A072351 12586269025,139583862445,1548008755920,10610209857723,
%U A072351 117669030460994,1304969544928657,14472334024676221,160500643816367088,1100087778366101931,12200160415121876738
%N A072351 Smallest n-digit Fibonacci number.
%H A072351 Alois P. Heinz, <a href="/A072351/b072351.txt">Table of n, a(n) for n = 1..1000</a>
%F A072351 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
%e A072351 a(3)=144, as 144 is smallest 3-digit Fibonacci number.
%p A072351 F:= proc(n) option remember; local f;
%p A072351       f:= `if`(n=1, [1$2], F(n-1));
%p A072351       do f:= [f[2], f[1]+f[2]];
%p A072351          if length(f[1])<length(f[2]) then break fi
%p A072351       od; f
%p A072351     end:
%p A072351 a:= n-> `if`(n=1, 1, F(n-1)[2]):
%p A072351 seq(a(n), n=1..25);  # _Alois P. Heinz_, Mar 10 2016
%t A072351 a[n_] := Fibonacci[Ceiling[k /. FindRoot[Log[10, Fibonacci[k]] == n-1, {k, 1}]]]; Array[a, 20] (* _Jean-François Alcover_, Jan 18 2017 *)
%t A072351 With[{fbs=Fibonacci[Range[100]]},Table[SelectFirst[fbs,IntegerLength[#]==n&],{n,20}]] (* _Harvey P. Dale_, Dec 13 2024 *)
%o A072351 (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
%o A072351 (Python)
%o A072351 def A072351_list(n):
%o A072351     list = [1]
%o A072351     x, y = 1, 1
%o A072351     while len(list) < n:
%o A072351         if len(str(x)) < len(str(y)):
%o A072351             list.append(y)
%o A072351         x, y = y, x + y
%o A072351     return list
%o A072351 print(A072351_list(20)) # _M. Eren Kesim_, Jun 28 2021
%Y A072351 Cf. A072352, A105710, A105712, A105713, A105714, A105715, A105716, A105717, A105718, A105719.
%K A072351 base,nonn
%O A072351 1,2
%A A072351 _Shyam Sunder Gupta_, Jul 17 2002