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 A289035 Fixed point of the mapping 00->0010, 01->010, 10->010, starting with 00. 6
 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289004. The mapping is applied as in the Mathematica command StringReplace. In particular, for a word of odd length, the final letter is retained, as in 0010010 -> 00100100100. (If the final letter is removed, the iterates are changed, but the limiting fixed point remains unchanged. See A293077.) More generally, to describe the result of the command StringReplace[w, {u(1)->v(1), u(2)->v(2) ... u(n)-3. - Michel Dekking, Mar 20 2022 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE First seven iterates of the mapping: 00 0010 0010010 00100100100 001001001000100100 0010010010001001000100100100010 0010010010001001000100100100010010001001001000100100 MATHEMATICA z = 10; (* number of iterates *) s = {0, 0}; w[0] = StringJoin[Map[ToString, s]]; w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "010"}] TableForm[Table[w[n], {n, 0, 10}]] st = ToCharacterCode[w[z]] - 48 (* A289035 *) Flatten[Position[st, 0]] (* A289036 *) Flatten[Position[st, 1]] (* A289037 *) Table[StringLength[w[n]], {n, 0, 20}] (* A289004 *) CROSSREFS Cf. A289036, A289037, A289004, A293076. Sequence in context: A286748 A289001 A171588 * A276397 A286747 A131531 Adjacent sequences: A289032 A289033 A289034 * A289036 A289037 A289038 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 27 2017 EXTENSIONS Updated by Clark Kimberling, Sep 30 2017 STATUS approved

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Last modified August 13 01:30 EDT 2024. Contains 375113 sequences. (Running on oeis4.)