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 A288736 2-limiting word of the mapping 00->1000, 10->01, starting with 00. 5
 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 (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 2-limiting word is the limit of the n-th iterates for n == 2 mod 4.  Conjecture: the number of letters (0s and 1s) 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 == 2 mod 3 are 011000 011000011011011000 011000011011011000011000011011011011011000 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[22]] - 48   (* A288736 *) Flatten[Position[st, 0]]  (* A288737 *) Flatten[Position[st, 1]]  (* A288740 *) CROSSREFS Cf. A288729 (0-limiting word), A288737, A288740, A288733 (1-limiting word), A288741 (3-limiting word). Sequence in context: A125720 A095130 A284789 * A270803 A030301 A316341 Adjacent sequences:  A288733 A288734 A288735 * A288737 A288738 A288739 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 16 2017 STATUS approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)