%I A065019
%S A065019 1,3,5,11,11,13,15,17,19,21,25,27,29,31,35,35,39,41,45,49,49,51,53,55,
%T A065019 57,61,63,65,67,69,73,75,77,81,83,83,87,91,95,95,99,99,103,103,105,107,
%U A065019 113,113,115,117,121,123,125,129,131,133,135,137,139,141,143,147,149
%N A065019 Let phi be the golden number {1+sqrt(5)}/2 (A001622), let phi(n) be the 
               number phi written in base 10 but truncated to n decimal digits. 
               Sequence gives number of 1's at the beginning of the continued fraction 
               expansion of phi(n).
%C A065019 a(n) has the curious property of always being odd but is otherwise quite 
               random. Nevertheless c = lim(n -> infinity) a(n)/n exists, about 
               2.3926 +/- 0.0004.
%F A065019 The value of lim n -> infinity a(n)/n is ln(10)/2/ln(phi)=2, 3924...
%e A065019 phi(6)=1.618033. The continued fraction expansion of phi(6) = {1, 1, 
               1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 129}. Hence a(6) = 
               15.
%t A065019 gr = RealDigits[ N[ GoldenRatio, 250]] [[1]]; f[n_] := Block[ {k = 1}, 
               While[ ContinuedFraction[ FromDigits[ {Take[ gr, n + 1 ], 1} ]] [[k]] 
               == 1, k++ ]; k - 1]; Table[ f[n], {n, 0, 70} ]
%Y A065019 Cf. A001622.
%Y A065019 Sequence in context: A129738 A105603 A122133 this_sequence A071328 A006538 
               A066281
%Y A065019 Adjacent sequences: A065016 A065017 A065018 this_sequence A065020 A065021 
               A065022
%K A065019 nonn,base
%O A065019 0,2
%A A065019 Benoit Cloitre (benoit7848c(AT)orange.fr) and Boris Gourevitch (boris(AT)314.net), 
               Nov 02 2001
%E A065019 Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 02 
               2001