Search: id:A079101
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%I A079101
%S A079101 0,1,0,0,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0,
%T A079101 0,0,1,1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,
%U A079101 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.
%D A079101 C. Kimberling, Problem 2289, Crux Mathematicorum 23 (1997) 501.
%H A079101 A. Dau <a href="http://comunidad.ciudad.com.ar/argentina/buenos_aires/
               avd/subsub.html">Secuencia Maximizadora de Subcadenas (Interactive 
               Javagenerator of repetition-resistant sequences)</a>.
%H A079101 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/unsolved.html">
               Unsolved Problems and Rewards</a>.
%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.
%Y A079101 Sequence in context: A134667 A117943 A096268 this_sequence A076478 A091444 
               A091447
%Y A079101 Adjacent sequences: A079098 A079099 A079100 this_sequence A079102 A079103 
               A079104
%K A079101 nonn
%O A079101 1,1
%A A079101 Clark Kimberling (ck6(AT)evansville.edu), Jan 03 2003

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