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%I #18 Feb 14 2024 12:38:28
%S 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 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 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 A repetition-resistant sequence.
%C a(n) = 0 or 1, chosen so as to maximize the number of different subsequences that are formed.
%C 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 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 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 Differs from A334941 for the first time at n = 70. - _Jeffrey Shallit_, Dec 14 2022
%H Peter J. C. Moses, <a href="/A079101/b079101.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/unsolved.html">Unsolved Problems and Rewards</a>.
%H Clark Kimberling, <a href="https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv23n8.pdf">Problem 2289</a>, Crux Mathematicorum 23 (1997) 501.
%e 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 Cf. A079136, A079335, A079336, A079337, A079338, A007061, A334941.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 03 2003
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