%I A093382
%S A093382 11,31,199
%N A093382 a(n) = length k of longest binary sequence x(1) ... x(k) such that for 
               no n <= i < j <= k/2 is x(i) ... x(2i) a subsequence of x(j) ... 
               x(2j).
%C A093382 Doesn't the binary sequence 000010011001110011101010101010101010101100110 
               demonstrate that a(2)>=45 ? - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 29 2007 Answer: No - see the following comment.
%C A093382 The sequence of length 45 above does not satisfy the requirements of 
               the definition: Subsequences are not required to be consecutive. 
               Therefore it cannot show a(2)>=45. In the sequence we find for i=2, 
               j=3: x(i..2i) is 000; x(j..2j) is 001001; and 000 is a subsequence 
               of 001001. - Don Reble (djr(AT)nk.ca), May 13 2008
%D A093382 a(1) - a(3) computed by R. Dougherty, who finds that a(4) >= 187205.
%H A093382 H. M. Friedman, <a href="http://www.math.ohio-state.edu/%7Efriedman/pdf/
               finiteseq10_8_98.pdf">Long finite sequences</a>, J. Comb. Theory, 
               A 95 (2001), 102-144.
%e A093382 a(1) = 11 from 01110000000.
%Y A093382 See A093383-A093386 for illustrations of a(2) and a(3). Cf. A014221, 
               A094091.
%Y A093382 Sequence in context: A144727 A002535 A128337 this_sequence A098264 A023279 
               A068715
%Y A093382 Adjacent sequences: A093379 A093380 A093381 this_sequence A093383 A093384 
               A093385
%K A093382 nonn,bref,nice,more
%O A093382 1,1
%A A093382 N. J. A. Sloane (njas(AT)research.att.com), Apr 29 2004