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%I #10 Sep 07 2014 12:49:39
%S 0,0,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0
%N a(1) = 0; for n>0, a(n) = smaller of 0 and 1 such that we avoid the property that, for some i and j in the range S = 2 <= i < j <= n/2, a(i) ... a(2i) is a subsequence of a(j) ... a(2j).
%C A greedy version of A093383 and A093384.
%C This is a finite sequence of length 23 (necessarily <= A093382(2) = 31).
%C For S >= 1 define a sequence by a(1) = 0; for n>0, a(n) = smaller of 0 and 1 such that we avoid the property that, for some i and j in the range S <= i < j <= n/2, a(i) ... a(2i) is a subsequence of a(j) ... a(2j). The present sequence is the case S=2. For S=1 we get a sequence of length 3, namely 0,0,0, and A096094, A106197 are the cases S=3 and S=4. A093382(S) gives an upper bound on their lengths.
%H H. M. Friedman, <a href="http://dx.doi.org/10.1006/jcta.2000.3154">Long finite sequences</a>, J. Comb. Theory, A 95 (2001), 102-144.
%e After a(1) = a(2) = a(3) = a(4) = 0 we must have a(5) = 1, or else we would have a(2)a(3)a(4) = 000 as a subsequence of a(3)a(4)a(5)a(6) = 000a(6).
%Y Cf. A093382, A093383, A093384, A096094, A106197.
%K nonn,fini,full,easy
%O 1,1
%A _N. J. A. Sloane_, May 02 2004
%E The remaining terms, a(17)-a(23), were sent by _Joshua Zucker_, Jul 23 2006
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