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 A359838 #20 Feb 16 2023 05:37:47
%S A359838 0,1,3,3,1,2,1,262143,3,1,3,3,1,
%T A359838 1532495540865888858358347027150309183618739122183602175,4,3,1,3,
%U A359838 262143,1,2,1,3,3,1
%N A359838 Continued fraction for binary expansion of A359456 interpreted in base 2.
%C A359838 The continued fraction of the number obtained by reading A359456 as a binary fraction.
%C A359838 Except for the first term, the only values that occur in this sequence are 1, 2, 3, 4 and values 2^A359458(m) - 1 for m > 2. The probabilities of occurrence P(a(n) = k) are given by:
%C A359838 P(a(n) = 1) = 1/3,
%C A359838 P(a(n) = 2) = 1/12,
%C A359838 P(a(n) = 3) = 1/3,
%C A359838 P(a(n) = 4) = 1/12 and
%C A359838 P(a(n) = 2^A359458(m)-1) = 1/(3*2^m) for m > 1.
%F A359838 a(n) = 1 if and only if n in A317538.
%F A359838 a(n) = 2 if and only if n in {24*m - 19 | m > 0} union {24*m - 4 | m > 0}.
%F A359838 a(n) = 3 if and only if n in A317539.
%F A359838 a(n) = 4 if and only if n in {12*m - 3*A014710(m-1) + 5 | m > 0}
%F A359838 a(n) = 2^A359458(m)-1 if and only if n in {3*2^(m-1)*(1+k*4) + 1 | k >= 0} union {3*2^(m-1)*(3+k*4) | k >= 0} for m > 1.
%Y A359838 Cf. A014710, A317538, A317539, A359456, A359458.
%Y A359838 Cf. A359457 (in base 10).
%K A359838 nonn,base,cofr
%O A359838 0,3
%A A359838 _A.H.M. Smeets_, Jan 14 2023