The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A287267 1-limiting word of the morphism 0->11, 1->02, 2->0. 5
 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Starting with 0, the first 5 iterations of the morphism yield words shown here: 1st:  11 2nd:  0202 3rd:  110110 4th:  020211020211 5th:  11011002021101100202 The 1-limiting word is the limit of the words for which the number of iterations is odd. 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 = 2.7692923542386314152404094643350334926..., V = 2.4498438945029551040577327454145475624..., W = 4.3344900716222708116779374775820643087... If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,5,6,10}, and w(n) - w(n-1) is in {2,4,8,10,16}. From Michel Dekking, Oct 09 2019: (Start) Let u, v and w be the positions of 0, 1 and 2 in this sequence. The incidence matrix of the defining morphism: 0->10, 1->12, 2->0 has characteristic polynomial chi(u) = u^3 - 2u - 2. Let Q = [27+ 3*sqrt(57)]^(1/3). Then the real root of the characteristic polynomial chi is lambda :=  Q/3 + 2/Q. An eigenvector of lambda is (1, lambda^2-2, -lambda^2+lambda+2). The Perron-Frobenius Theorem then gives that the asymptotic frequencies f0, f1 and f2 of the letters 0, 1, and 2 are f0 = 1/(1+lambda), f1 = (lambda^2-2)/(1+lambda), and f2 = (-lambda^2+lambda+2)/(1+lambda). Algebraic expressions for the three constants U, V and W are then given by U = 1/f0, V = 1/f1, W = 1/f2. (End) LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE 3rd iterate: 110110; 5th iterate: 11011002021101100202. MATHEMATICA s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 2}, 2 -> 0}] &, {0}, 11] (* A287267 *) Flatten[Position[s, 0]] (* A287268 *) Flatten[Position[s, 1]] (* A287269 *) Flatten[Position[s, 2]] (* A287270 *) CROSSREFS Cf. A287263 (0-limiting word), A287268, A287269, A287270. Sequence in context: A235168 A060950 A039976 * A317540 A133701 A230417 Adjacent sequences:  A287264 A287265 A287266 * A287268 A287269 A287270 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 24 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 10 15:45 EDT 2020. Contains 335577 sequences. (Running on oeis4.)