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 A143589 #6 Jan 16 2013 18:51:55 %S A143589 1,2,1,1,2,1,1,1,2,2,1,2,2,1,1,2,1,1,2,2,2,1,2,2,1,2,1,1,2,2,1,1,2,1, %T A143589 1,2,2,1,2,2,1,2,1,1,2,2,2,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,1,2,1,2,2, %U A143589 1,1,1,1,2,1,1,2,2,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,1,1,2,2,1 %N A143589 Kolakoski fan based on A000034 with initial row 1. %C A143589 Conjecture (following Benoit Cloitre's conjecture at A111090): if L(n) is the number (assumed finite) of terms in row n of K, then L(n)*(2/3)^n approaches a constant. (L= A143590.) %F A143589 Introduced here is an array K called the "Kolakoski fan based on a sequence s with initial row w": suppose that s=(s(1),s(2),...) is a sequence of 1's and 2's and that w=(w(1),w(2),...) is a finite or infinite sequence of 1's and 2's. Assume that s(1)=w(1) and that if w(1)=1 then s contains at least one 2. Row 1 of the array K is w. Subsequent rows are defined inductively: the first term of row n is s(n) and the remaining terms are defined by Kolakoski substitution; viz., each number in row n-1 tells the string-length (1 or 2) of the next string in row n, each term being either 1 or 2. %e A143589 s=(1,2,1,2,1,2,1,2,...) and w=1, so the first 7 rows are %e A143589 1 %e A143589 2 %e A143589 1 1 %e A143589 2 1 %e A143589 1 1 2 %e A143589 2 1 2 2 %e A143589 1 1 2 1 1 2 2 %Y A143589 Cf. A000002, A143477, A143490. %K A143589 nonn,tabf %O A143589 1,2 %A A143589 _Clark Kimberling_, Aug 25 2008