A282244 Lexicographic block-fractal zero-one word with initial block 01.

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, 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, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1

Offset

1

Comments

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.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Mathematica

str = "01"; t = Table[str = str <> StringJoin[Map[#[[1]] &,
Select[Map[{#, Length[StringPosition[str, #, 1]] > 0} &,
Table[StringJoin[Map[ToString, IntegerDigits[n, 2, k]]], {n,
0, 2^k - 1}]], ! #[[2]] &]]], {k, 7}]
ToExpression[Characters[Last[t]]]  (* _Peter J. C. Moses, Mar 11 2017 *)

Crossrefs

Cf. A280511.

Sequence in context: A357448 A083651 A111748 * A286691 A359172 A288462

Adjacent sequences: A282241 A282242 A282243 * A282245 A282246 A282247

Keyword

nonn,easy

Author

Clark Kimberling, Mar 16 2017

Status

approved