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 A079101 #18 Feb 14 2024 12:38:28 %S A079101 0,1,0,0,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0, %T A079101 0,0,0,1,1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,1,0, %U A079101 0,0,1,1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0 %N A079101 A repetition-resistant sequence. %C A079101 a(n) = 0 or 1, chosen so as to maximize the number of different subsequences that are formed. %C A079101 a(n+1)=1 if and only if (a(1),a(2),...,a(n),0), but not (a(1),a(2),...,a(n),1), has greater length of longest repeated segment than (a(1),a(2),...,a(n)) has. %C A079101 In Feb, 2003, Alejandro Dau solved Problem 3 on the Unsolved Problems and Rewards website, thus establishing that every binary word occurs infinitely many times in this sequence. %C A079101 Klaus Sutmer remarks (Jun 26 2006) that this sequence is very similar to the Ehrenfeucht-Mycielski sequence A007061. Both sequences have every finite binary word as a factor; in fact, essentially the same proof works for both sequences. %C A079101 Differs from A334941 for the first time at n = 70. - _Jeffrey Shallit_, Dec 14 2022 %H A079101 Peter J. C. Moses, <a href="/A079101/b079101.txt">Table of n, a(n) for n = 1..10000</a> %H A079101 A. Dau, <a href="http://comunidad.ciudad.com.ar/argentina/buenos_aires/avd/subsub.html">Secuencia Maximizadora de Subcadenas (Interactive Java generator of repetition-resistant sequences)</a>. [Broken link] %H A079101 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/unsolved.html">Unsolved Problems and Rewards</a>. %H A079101 Clark Kimberling, <a href="https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv23n8.pdf">Problem 2289</a>, Crux Mathematicorum 23 (1997) 501. %e A079101 a(7)=1 because (0,1,0,0,0,1,0) has repeated segment (0,1,0) of length 3, whereas (0,1,0,0,0,1,1) has no repeated segment of length 3. %Y A079101 Cf. A079136, A079335, A079336, A079337, A079338, A007061, A334941. %K A079101 nonn %O A079101 1,1 %A A079101 _Clark Kimberling_, Jan 03 2003