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%I #13 Oct 26 2020 17:32:30
%S 5,10,29,34,53,58,77,96,101,120,125,139,144,163,168,187,192,206,211,
%T 230,235,254,273,278,297,302,321,340,345,364,369,388,407,412,431,436,
%U 455,474,479,498,503,522,541,546,565,570,584,589,608,613,632,637,651,656
%N Numbers n such that 5 is the leading digit of the n-th Fibonacci number in decimal representation.
%C A008963(a(n)) = 5; A105515(a(n)) = A105515(a(n) - 1) + 1.
%H Robert Israel, <a href="/A105505/b105505.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(6) - log(5)) = 12.629253.... - _Charles R Greathouse IV_, Oct 07 2016
%e a(10)=120: A008963(120) = A000030(A000045(120)) =
%e A000030(5358359254990966640871840) = 5.
%p ld:= x -> floor(x/10^ilog10(x)):
%p select(n -> ld(combinat:-fibonacci(n))=5, [$1..1000]); # _Robert Israel_, Oct 26 2020
%t Select[Range[700],First[IntegerDigits[Fibonacci[#]]]==5&] (* _Harvey P. Dale_, Jul 31 2018 *)
%o (PARI) is(n)=digits(fibonacci(n))[1]==5 \\ _Charles R Greathouse IV_, Oct 07 2016
%Y Cf. A000030, A000045, A072703, A105501, A105502, A105503, A105504, A105506, A105507, A105508, A105509.
%K nonn,base
%O 1,1
%A _Reinhard Zumkeller_, Apr 11 2005
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