This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065019 #11 Jul 10 2015 00:39:14
%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,
%U A065019 107,113,113,115,117,121,123,125,129,131,133,135,137,139,141,143,147,149
%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 log(10)/2/log(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.
%K A065019 nonn,base
%O A065019 0,2
%A A065019 _Benoit Cloitre_ and Boris Gourevitch (boris(AT)314.net), Nov 02 2001
%E A065019 Additional comments from _Robert G. Wilson v_, Nov 02 2001