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A164018
The index values of the smallest and the largest n-digit Fibonacci numbers.
1
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
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