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A105501 Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.

%I A105501 #10 May 02 2018 22:35:19
%S A105501 1,2,7,12,17,21,22,26,27,31,36,40,41,45,46,50,55,60,64,65,69,70,74,79,
%T A105501 84,88,89,93,94,98,103,107,108,112,113,117,122,127,131,132,136,137,
%U A105501 141,146,151,155,156,160,161,165,170,174,175,179,180,184,189,194,198,199
%N A105501 Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.
%C A105501 A008963(a(n)) = 1; A105511(a(n)) = A105511(a(n) - 1) + 1.
%H A105501 Robert Israel, <a href="/A105501/b105501.txt">Table of n, a(n) for n = 1..10000</a>
%F A105501 a(n) ~ kn by the equidistribution theorem, where k = log(10)/log(2) = 3.321928.... - _Charles R Greathouse IV_, Oct 07 2016
%e A105501 a(10)=31: A008963(31) = A000030(A000045(31)) =
%e A105501 A000030(1346269) = 1.
%p A105501 filter:= proc(n) local t;
%p A105501   t:= combinat:-fibonacci(n);
%p A105501   t < 2*10^ilog10(t)
%p A105501 end proc:
%p A105501 select(filter, [$1..200]); # _Robert Israel_, May 02 2018
%t A105501 fQ[n_] := IntegerDigits[Fibonacci[n]][[1]] == 1; Select[Range@200, fQ] (* _Robert G. Wilson v_, May 02 2018 *)
%o A105501 (PARI) is(n)=digits(fibonacci(n))[1]==1 \\ _Charles R Greathouse IV_, Oct 07 2016
%Y A105501 Cf. A000030, A000045, A072675, A105502, A105503, A105504, A105505, A105506, A105507, A105508, A105509.
%K A105501 nonn,base
%O A105501 1,2
%A A105501 _Reinhard Zumkeller_, Apr 11 2005