A072354 a(n)-th Fibonacci number is the smallest Fibonacci number containing n digits.

1, 7, 12, 17, 21, 26, 31, 36, 40, 45, 50, 55, 60, 64, 69, 74, 79, 84, 88, 93, 98, 103, 107, 112, 117, 122, 127, 131, 136, 141, 146, 151, 155, 160, 165, 170, 174, 179, 184, 189, 194, 198, 203, 208, 213, 217, 222, 227, 232, 237

Offset: 1

Author

Shyam Sunder Gupta, Jul 18 2002

Keywords

• base
• nonn

Examples

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

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20899

Crossrefs

Cf. A001622, A105700, A105702, A105703, A105704, A105705, A105706, A105707, A105708, A105709.

Programs

Mathematica

Flatten[Table[Position[IntegerLength[Fibonacci[Range[250]]],n,{1},1],{n,50}]] (* Harvey P. Dale, Dec 22 2015 *)

PARI

a(n)={my(k=1); while(logint(fibonacci(k),10)Harry J. Smith, Nov 29 2008

Formula

For n>1, a(n) = A072353(n-1) + 1. - Michel Marcus, Jun 01 2014

For n>1, a(n) = ceiling(n*log(10)/log(phi)-log(20)/(2*log(phi))), where phi=(1+sqrt(5))/2, the golden ratio. - Hans J. H. Tuenter, Jul 13 2025