A105505 Numbers n such that 5 is the leading digit of the n-th Fibonacci number in decimal representation.

5, 10, 29, 34, 53, 58, 77, 96, 101, 120, 125, 139, 144, 163, 168, 187, 192, 206, 211, 230, 235, 254, 273, 278, 297, 302, 321, 340, 345, 364, 369, 388, 407, 412, 431, 436, 455, 474, 479, 498, 503, 522, 541, 546, 565, 570, 584, 589, 608, 613, 632, 637, 651, 656

Offset

1,1

Comments

A008963(a(n)) = 5; A105515(a(n)) = A105515(a(n) - 1) + 1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(6) - log(5)) = 12.629253.... - Charles R Greathouse IV, Oct 07 2016

Example

a(10)=120: A008963(120) = A000030(A000045(120)) =
A000030(5358359254990966640871840) = 5.

Maple

ld:= x -> floor(x/10^ilog10(x)):
select(n -> ld(combinat:-fibonacci(n))=5, [$1..1000]); # Robert Israel, Oct 26 2020

Mathematica

Select[Range[700], First[IntegerDigits[Fibonacci[#]]]==5&] (* Harvey P. Dale, Jul 31 2018 *)

Prog

(PARI) is(n)=digits(fibonacci(n))[1]==5 \\ Charles R Greathouse IV, Oct 07 2016

Crossrefs

Cf. A000030, A000045, A072703, A105501, A105502, A105503, A105504, A105506, A105507, A105508, A105509.

Sequence in context: A105862 A338662 A093029 * A005514 A069921 A053818

Adjacent sequences: A105502 A105503 A105504 * A105506 A105507 A105508

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved