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%I #7 Apr 13 2019 17:31:21
%S 4,9,14,28,33,38,52,57,71,76,81,95,100,105,119,124,138,143,148,162,
%T 167,172,181,186,191,205,210,215,229,234,239,248,253,258,272,277,282,
%U 296,301,306,315,320,325,339,344,349,363,368,382,387,392,406,411,416,430
%N Numbers n such that 3 is the leading digit of the n-th Fibonacci number in decimal representation.
%C A008963(a(n)) = 3; A105513(a(n)) = A105513(a(n) - 1) + 1.
%F a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(4) - log(3)) = 8.00392.... - _Charles R Greathouse IV_, Oct 07 2016
%e a(10)=76: A008963(76) = A000030(A000045(76)) =
%e A000030(3416454622906707) = 3.
%t Select[Table[{n,Fibonacci[n]},{n,450}],First[IntegerDigits[#[[2]]]]==3&][[All,1]] (* _Harvey P. Dale_, Apr 13 2019 *)
%o (PARI) is(n)=digits(fibonacci(n))[1]==3 \\ _Charles R Greathouse IV_, Oct 07 2016
%Y Cf. A000030, A000045, A072683, A105501, A105502, A105504, A105505, A105506, A105507, A105508, A105509.
%K nonn,base
%O 1,1
%A _Reinhard Zumkeller_, Apr 11 2005
%E Definition clarified by _Harvey P. Dale_, Apr 13 2019