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 A227339 Fixed point of the morphism 1 -> 131, 2 -> 312, 3 -> 2. 0
 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Counterexample by Labbé to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes. In the paper cited, the fixed point is given as acabacacabacab..., this sequence uses 1 for a, 2 for b, and 3 for c. LINKS Table of n, a(n) for n=1..121. A. Hof, O. Knill, and B. Simon, Singular continuous spectrum for palindromic Schrödinger operators, Comm. Math. Phys., 174 (1995) number 1, pp 149-159. Sébastien Labbé, A counterexample to a question of Hof, Knill and Simon, arXiv:1307.1589v1 [math.CO], Jul 05 2013 EXAMPLE Start: 1 Rules: 1 --> 131 2 --> 312 3 --> 2 ------------- 0: (#=1) 1 1: (#=3) 131 2: (#=7) 1312131 3: (#=17) 13121313121312131 4: (#=41) 13121313121312131213131213121313121312131 5: (#=99) 1312131312131213121313121312... 6: (#=239) 1312131312131213121313121312... 7: (#=577) 1312131312131213121313121312... - Joerg Arndt, Jul 08 2013 MATHEMATICA Nest[Flatten[# /. {1 -> {1, 3, 1}, 2 -> {3, 1, 2}, 3 -> {2}}] &, {1}, 5] (* Robert G. Wilson v, Nov 05 2015 *) CROSSREFS Cf. A010060. Sequence in context: A361019 A157520 A325116 * A030777 A353375 A056595 Adjacent sequences: A227336 A227337 A227338 * A227340 A227341 A227342 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Jul 07 2013 EXTENSIONS More terms from Joerg Arndt, Jul 08 2013 STATUS approved

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Last modified September 14 09:44 EDT 2024. Contains 375921 sequences. (Running on oeis4.)