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 A288733 1-limiting word of the mapping 00->1000, 10->01, starting with 00. 6
 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Iterates of the mapping, starting with 00: 00 1000 011000 01011000 0011011000 10001011011000 011000011011011000 0101100001011011011000 00110110000011011011011000 1000101101100010001011011011011000 The 1-limiting word is the limit of the n-th iterates for n == 1 mod 4.  Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288732(n), for n >= 0. LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE The first three n-th iterates for n == 1 mod 3 are 1000 10001011011000 1000101101100010001011011011011000 MATHEMATICA s = {0, 0}; w[0] = StringJoin[Map[ToString, s]]; w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}] Table[w[n], {n, 0, 8}] st = ToCharacterCode[w[21]] - 48   (* A288733 *) Flatten[Position[st, 0]]  (* A288734 *) Flatten[Position[st, 1]]  (* A288735 *) Table[StringLength[w[n]], {n, 0, 20}] (* A288732 *) CROSSREFS Cf. A288729 (0-limiting word), A288734, A288735, A288732,  A288736 (2-limiting word), A288741 (3-limiting word). Sequence in context: A266444 A267679 A267868 * A095111 A166253 A159638 Adjacent sequences:  A288730 A288731 A288732 * A288734 A288735 A288736 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 16 2017 STATUS approved

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Last modified September 22 10:15 EDT 2020. Contains 337289 sequences. (Running on oeis4.)