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%I #7 Oct 18 2017 11:44:56
%S 0,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,1,1,1,1,0,
%T 0,0,0,0,0,0,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,
%U 1,1,0,1,0,1,1,1,1,0,1,1,1,1,1,0,0,1
%N Lexicographic block-fractal zero-one word with initial block 01.
%C To the initial block, 01, append the lexicographically ordered missing 2-letter words (00,10,11) to get 01001011. To that, append the missing 3-letter words to get 01001011000110111. To that, append the missing 4-letter words to get 010010110001101110000101011101111, etc. In the limiting word, every finite binary word occurs infinitely many times; thus, the word (or sequence) is block-fractal, as defined at A280511.
%H Clark Kimberling, <a href="/A282244/b282244.txt">Table of n, a(n) for n = 1..10000</a>
%t str = "01"; t = Table[str = str <> StringJoin[Map[#[[1]] &,
%t Select[Map[{#, Length[StringPosition[str, #, 1]] > 0} &,
%t Table[StringJoin[Map[ToString, IntegerDigits[n, 2, k]]], {n,
%t 0, 2^k - 1}]], ! #[[2]] &]]], {k, 7}]
%t ToExpression[Characters[Last[t]]] (* _Peter J. C. Moses, Mar 11 2017 *)
%Y Cf. A280511.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Mar 16 2017
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