A282244 - OEIS

%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