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 A287234 0-limiting word of the morphism 0->01, 1->20, 2->1, with initial term 1. 5
 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Starting with 0, the first 5 iterations of the morphism yield words shown here: 1st: 20 2nd: 101 3rd: 200120 4th: 1010120101 5th: 2001200120101200120 The 0-limiting word is the limit of the words for which the number of iterations is even. Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where U = 2.246979603717467061050009768008..., V = 2.801937735804838252472204639014..., W = 5.048917339522305313522214407023... If n >=2, then u(n) - u(n-1) is in {1,2,3}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,5,7}. LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE 2nd iterate: 101 4th iterate: 1010120101 6th iterate: 101012010101201012001201010120101 MATHEMATICA s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 0}, 2 -> 1}] &, {1}, 10] (* A287234 *) Flatten[Position[s, 0]] (* A287235 *) Flatten[Position[s, 1]] (* A287236 *) Flatten[Position[s, 2]] (* A287237 *) CROSSREFS Cf. A287002 (initial 0 instead of 1), A287235, A287236, A287237, A287240 (1-limiting word). Sequence in context: A364389 A116927 A137276 * A309938 A140581 A137277 Adjacent sequences: A287231 A287232 A287233 * A287235 A287236 A287237 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 23 2017 STATUS approved

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Last modified June 18 20:38 EDT 2024. Contains 373487 sequences. (Running on oeis4.)