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

Author

Reinhard Zumkeller, Apr 11 2005

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

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