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
Examples
a(10)=76: A008963(76) = A000030(A000045(76)) = A000030(3416454622906707) = 3.
Crossrefs
Programs
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Mathematica
Select[Table[{n,Fibonacci[n]},{n,450}],First[IntegerDigits[#[[2]]]]==3&][[All,1]] (* Harvey P. Dale, Apr 13 2019 *) -
PARI
is(n)=digits(fibonacci(n))[1]==3 \\ Charles R Greathouse IV, Oct 07 2016
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
Extensions
Definition clarified by Harvey P. Dale, Apr 13 2019
Comments