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 A288724 #37 Jan 17 2019 22:50:27 %S A288724 2,2,2,3,1,1,2,2,3,3,3,1,1,1,2,3,1,2,2,3,3,1,1,2,2,2,3,1,1,2,2,2,3,3, %T A288724 3,1,2,3,1,1,2,2,2,3,1,2,2,3,3,1,1,1,2,2,2,3,3,3,1,2,3,1,1,2,2,3,3,1, %U A288724 1,1,2,3,3,1,1,1,2,2,2,3,1,2,2,3,3,1,1 %N A288724 Second sequence of a Kolakoski 3-Ouroboros, i.e., sequence of 1s, 2s and 3s that is second in a chain of three distinct sequences where successive run-length encodings produce seq(1) -> seq(2) -> seq(3) -> seq(1). %C A288724 See comments at A288723. %H A288724 Georg Fischer, <a href="/A288724/b288724.txt">Table of n, a(n) for n = 1..2000</a> (recovered b-file, Jan 16 2019) %H A288724 Rémy Sigrist, <a href="/A288724/a288724.gp.txt">PARI program for A288723, A288724 and A288725</a> %e A288724 Write down the run-lengths of the sequence A288723, or the lengths of the runs of 1s, 2s and 3s. This yields a second and different sequence of 1s, 2s and 3s, A288724 (as above). The run-lengths of this second sequence yield a third and different sequence, A288725. The run-lengths of this third sequence yield the original sequence. For example, bracket the runs of distinct integers, then replace the original digits with the run-lengths to create the second sequence: %e A288724 (1,1), (2,2), (3,3), (1,1,1), (2), (3), (1,1), (2,2), (3,3,3), (1,1,1), (2,2,2), (3), (1), (2), (3,3), (1,1,1), (2), (3,3), (1,1), (2,2,2), ... -> 2, 2, 2, 3, 1, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 3, 1, 2, 2, 3, ... %e A288724 Apply the same process to the second sequence and the third sequence appears: %e A288724 (2,2,2), (3), (1,1), (2,2), (3,3,3), (1,1,1), (2), (3), (1), (2,2), (3,3), (1,1), (2,2,2), (3), (1,1), (2,2,2), (3,3,3), (1), (2), (3), ... -> 3, 1, 2, 2, 3, 3, 1, 1, 1, 2, 2, 2, 3, 1, 2, 3, 3, 1, 1, 1, ... %e A288724 Apply the same process to the third sequence and the original sequence reappears: %e A288724 (3), (1), (2,2), (3,3), (1,1,1), (2,2,2), (3), (1), (2), (3,3), (1,1,1), (2), (3), (1,1), (2,2), (3,3,3), (1,1,1), (2,2,2), (3), (1), ... -> 1, 1, 2, 2, 3, 3, 1, 1, 1, 2, 3, 1, 1, 2, 2, 3, 3, 3, 1, 1, ... %o A288724 (PARI) See Links section. %Y A288724 Cf. A000002, A025142, A025143. A288723 and A288725 are the first and third sequences in this 3-Ouroboros. %K A288724 nonn %O A288724 1,1 %A A288724 _Anthony Sand_, Jun 14 2017 %E A288724 Data corrected by _Rémy Sigrist_, Oct 07 2017