A105503 - OEIS

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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

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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.