%I #17 Dec 25 2015 00:10:28

%S 1,7,12,17,21,26,31,36,40,45,50,55,60,64,69,74,79,84,88,93,98,103,107,

%T 112,117,122,127,131,136,141,146,151,155,160,165,170,174,179,184,189,

%U 194,198,203,208,213,217,222,227,232,237

%N a(n)-th Fibonacci number is the smallest Fibonacci number containing n digits.

%H Harry J. Smith, <a href="/A072354/b072354.txt">Table of n, a(n) for n = 1..20899</a>

%F For n>1, a(n) = floor(n*c) (+3) or (+2) where c=log(10)/log(Phi) and Phi is the golden ratio = (1+sqrt(5))/2. - _Benoit Cloitre_, Aug 21 2002

%F For n>1, a(n) = A072353(n-1) + 1. - _Michel Marcus_, Jun 01 2014

%e a(3) = 12 as the 12th Fibonacci number is the smallest Fibonacci number with 3 digits.

%t Flatten[Table[Position[IntegerLength[Fibonacci[Range[250]]],n,{1},1],{n,50}]] (* _Harvey P. Dale_, Dec 22 2015 *)

%o (PARI) digitsIn(x)=1+log(x)\log(10) {d=0; for(n=1,100000,x=fibonacci(n); digits = digitsIn(x); if (digits!=d,d = digits; write("b072354.txt", digits, " ", n);))} \\ _Harry J. Smith_, Nov 29 2008

%Y Cf. A105700, A105702, A105703, A105704, A105705, A105706, A105707, A105708, A105709.

%K base,nonn

%O 1,2

%A _Shyam Sunder Gupta_, Jul 18 2002