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 A359457 #24 Mar 24 2025 22:36:01
%S A359457 0,9,11,99,1,10,9,999999999999999999,1,8,10,1,99,11,9
%N A359457 Continued fraction for constant A359456.
%C A359457 It seems that all terms smaller than 100 are identical to the continued fraction terms of Liouville's constant as in A058304.
%C A359457 Except for the first term, the only values that occur in this sequence are 1,8,9,10,11,and values 10^A359458(m-1)-1 for m > 1. The probability of occurrence P(a(n) = k) are given by:
%C A359457 P(a(n) = 1) = 1/4,
%C A359457 P(a(n) = 8) = 1/8,
%C A359457 P(a(n) = 9) = 1/8,
%C A359457 P(a(n) = 10) = 1/8,
%C A359457 P(a(n) = 11) = 1/8 and
%C A359457 P(a(n) = 10^A359458(m-1)-1) = 2^-(m+1) for m > 1.
%F A359457 a(n) = 1 if and only if n in A317331,
%F A359457 a(n) = 8 if and only if n in A317332,
%F A359457 a(n) = 9 if and only if n in A317333,
%F A359457 a(n) = 10 if and only if n = 8*m - 6 + 3*(m mod 2) for m > 0,
%F A359457 a(n) = 11 if and only if n = 8*m - 3 - 3*(m mod 2) for m > 0,
%F A359457 a(n) = 10^A359458(m-1)-1 if and only if n in {2^m*(1+k*4) - 1 | k >= 0} union {2^m*(3+k*4) | k >= 0} for m > 1.
%Y A359457 Cf. A058304, A317331, A317332, A317333, A359456, A359458.
%K A359457 nonn,cofr,more
%O A359457 0,2
%A A359457 _A.H.M. Smeets_, Jan 02 2023