A105503 Numbers n such that 3 is the leading digit of the n-th Fibonacci number in decimal representation.

4, 9, 14, 28, 33, 38, 52, 57, 71, 76, 81, 95, 100, 105, 119, 124, 138, 143, 148, 162, 167, 172, 181, 186, 191, 205, 210, 215, 229, 234, 239, 248, 253, 258, 272, 277, 282, 296, 301, 306, 315, 320, 325, 339, 344, 349, 363, 368, 382, 387, 392, 406, 411, 416, 430

Offset

1,1

Comments

A008963(a(n)) = 3; A105513(a(n)) = A105513(a(n) - 1) + 1.

Links

Table of n, a(n) for n=1..55.

Formula

a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(4) - log(3)) = 8.00392.... - Charles R Greathouse IV, Oct 07 2016

Example

a(10)=76: A008963(76) = A000030(A000045(76)) =
A000030(3416454622906707) = 3.

Mathematica

Select[Table[{n, Fibonacci[n]}, {n, 450}], First[IntegerDigits[#[[2]]]]==3&][[All, 1]] (* Harvey P. Dale, Apr 13 2019 *)

Prog

(PARI) is(n)=digits(fibonacci(n))[1]==3 \\ Charles R Greathouse IV, Oct 07 2016

Crossrefs

Cf. A000030, A000045, A072683, A105501, A105502, A105504, A105505, A105506, A105507, A105508, A105509.

Sequence in context: A073497 A244941 A086192 * A095169 A345407 A105703

Adjacent sequences: A105500 A105501 A105502 * A105504 A105505 A105506

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Extensions

Definition clarified by Harvey P. Dale, Apr 13 2019

Status

approved