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

1,2

Comments

A008963(a(n)) = 1; A105511(a(n)) = A105511(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(2) = 3.321928.... - Charles R Greathouse IV, Oct 07 2016

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A160455 A045929 A277598 * A016873 A019592 A220120

Adjacent sequences: A105498 A105499 A105500 * A105502 A105503 A105504

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved