A105501 - OEIS

%I #10 May 02 2018 22:35:19

%S 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 84,88,89,93,94,98,103,107,108,112,113,117,122,127,131,132,136,137,

%U 141,146,151,155,156,160,161,165,170,174,175,179,180,184,189,194,198,199

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

%C A008963(a(n)) = 1; A105511(a(n)) = A105511(a(n) - 1) + 1.

%H Robert Israel, <a href="/A105501/b105501.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ kn by the equidistribution theorem, where k = log(10)/log(2) = 3.321928.... - _Charles R Greathouse IV_, Oct 07 2016

%e a(10)=31: A008963(31) = A000030(A000045(31)) =

%e A000030(1346269) = 1.

%p filter:= proc(n) local t;

%p   t:= combinat:-fibonacci(n);

%p   t < 2*10^ilog10(t)

%p end proc:

%p select(filter, [$1..200]); # _Robert Israel_, May 02 2018

%t fQ[n_] := IntegerDigits[Fibonacci[n]][[1]] == 1; Select[Range@200, fQ] (* _Robert G. Wilson v_, May 02 2018 *)

%o (PARI) is(n)=digits(fibonacci(n))[1]==1 \\ _Charles R Greathouse IV_, Oct 07 2016

%Y Cf. A000030, A000045, A072675, A105502, A105503, A105504, A105505, A105506, A105507, A105508, A105509.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Apr 11 2005