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

1,2

Links

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

Formula

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A091215 A261410 A090067 * A091576 A364095 A272733

Adjacent sequences: A072351 A072352 A072353 * A072355 A072356 A072357

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 18 2002

Status

approved