A164018 The index values of the smallest and the largest n-digit Fibonacci numbers.

0, 6, 7, 11, 12, 16, 17, 20, 21, 25, 26, 30, 31, 35, 36, 39, 40, 44, 45, 49, 50, 54, 55, 59, 60, 63, 64, 68, 69, 73, 74, 78, 79, 83, 84, 87, 88, 92, 93, 97, 98, 102, 103, 106, 107, 111, 112, 116, 117, 121, 122, 126, 127, 130, 131, 135, 136, 140, 141, 145

Offset

1,2

Comments

A072354 and A072353 interleaved, apart from a(1). - Parthasarathy Nambi, Sep 14 2009

For n>0, a(2n)=A072353(n) and a(2n+1)=A072354(n+1). - Hans J. H. Tuenter, Sep 09 2025

Links

Hans J. H. Tuenter, Table of n, a(n) for n = 1..10000 (first 1000 terms by Harvey P. Dale)

Formula

For n>1, a(n) = floor(floor(n/2)*log(10)/log(phi)+log(5)/(2*log(phi))) + (n mod 2), where phi = (1+sqrt(5))/2 = A001622. - Hans J. H. Tuenter, Sep 09 2025

Example

The index value of the smallest ten-digit Fibonacci number is a(19) = 45. The index value of the largest ten-digit Fibonacci number is a(20) = 49.
The first term is the smallest 1-digit Fibonacci number, which is taken to be F(0) = 0, so that the index a(1) = 0. The second term is the largest 1-digit Fibonacci number, which is F(6) = 8, so that the index a(2) = 6. - Hans J. H. Tuenter, Sep 09 2025

Mathematica

Drop[Flatten[{#-1, #}&/@Flatten[Table[Position[IntegerLength[Fibonacci[ Range[250]]], n, 1, 1], {n, 50}]]], {2}](* Harvey P. Dale, Jun 04 2018 *)

Crossrefs

Cf. A000045, A001622, A072353 (even bisection), A072354 (odd bisection), A097348.

Sequence in context: A117618 A015825 A243489 * A156793 A081715 A054504

Adjacent sequences: A164015 A164016 A164017 * A164019 A164020 A164021

Keyword

base,nonn

Author

Parthasarathy Nambi, Aug 07 2009

Extensions

More terms from Harvey P. Dale, Jun 04 2018

Offset changed by Hans J. H. Tuenter, Sep 09 2025

Status

approved