A105501 Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.

1, 2, 7, 12, 17, 21, 22, 26, 27, 31, 36, 40, 41, 45, 46, 50, 55, 60, 64, 65, 69, 70, 74, 79, 84, 88, 89, 93, 94, 98, 103, 107, 108, 112, 113, 117, 122, 127, 131, 132, 136, 137, 141, 146, 151, 155, 156, 160, 161, 165, 170, 174, 175, 179, 180, 184, 189, 194, 198, 199

Offset: 1

Author

Reinhard Zumkeller, Apr 11 2005

Keywords

• nonn
• base

Comments

A008963(a(n)) = 1; A105511(a(n)) = A105511(a(n) - 1) + 1.

Examples

			a(10)=31: A008963(31) = A000030(A000045(31)) =
A000030(1346269) = 1.
		

Links

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

Crossrefs

Cf. A000030, A000045, A072675, A105502, A105503, A105504, A105505, A105506, A105507, A105508, A105509.

Programs

Maple

filter:= proc(n) local t;
  t:= combinat:-fibonacci(n);
  t < 2*10^ilog10(t)
end proc:
select(filter, [$1..200]); # Robert Israel, May 02 2018

Mathematica

fQ[n_] := IntegerDigits[Fibonacci[n]][[1]] == 1; Select[Range@200, fQ] (* Robert G. Wilson v, May 02 2018 *)

PARI

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

Formula

a(n) ~ kn by the equidistribution theorem, where k = log(10)/log(2) = 3.321928.... - Charles R Greathouse IV, Oct 07 2016