%I #8 Feb 14 2024 12:38:21

%S 0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,1,0,0,1,1,0,1,1,0,1,0,

%T 1,1,0,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,1,1,0,0,1,1,1,1,1,1,1,0,1,1,1,1,

%U 1,0,0,1,1,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,1,1

%N A repetition-resistant sequence.

%C Unsolved problem: is every finite binary sequence a segment of a?

%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.

%F a(n+1)=0 if and only if (a(1), a(2), ..., a(n), 1), but not (a(1), a(2), ..., a(n), 0), has greater length of longest repeated segment than (a(1), a(2), ..., a(n)) has.

%e a(8)=1 because (0,1,1,0,0,1,0,0) has repeated segment (1,0,0) of length 3, whereas (0,1,1,0,0,1,0,1) has no repeated segment of length 3.

%Y Cf. A079101, A079136, A079335, A079337, A079338.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 03 2003