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#21 by Bruno Berselli at Thu Oct 03 09:00:15 EDT 2019
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#20 by Michel Marcus at Thu Oct 03 08:55:56 EDT 2019
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#19 by Michel Marcus at Thu Oct 03 08:55:52 EDT 2019
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| REFERENCES
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Justin, Jacques, and Laurent Vuillon. "Return words in Sturmian and episturmian words." RAIRO-Theoretical Informatics and Applications 34.5 (2000): 343-356.
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| LINKS
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Jacques Justin and Laurent Vuillon, <a href="http://www.numdam.org/item/ITA_2000__34_5_343_0/">Return words in Sturmian and episturmian words</a>, RAIRO-Theoretical Informatics and Applications 34.5 (2000): 343-356.
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approved
editing
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#18 by N. J. A. Sloane at Mon Sep 23 10:59:00 EDT 2019
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#17 by N. J. A. Sloane at Mon Sep 23 10:58:57 EDT 2019
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[See Justin & Vuillon (2000) for definition of return word. - N. J. A. Sloane, Sep 23 2019]
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| REFERENCES
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Justin, Jacques, and Laurent Vuillon. "Return words in Sturmian and episturmian words." RAIRO-Theoretical Informatics and Applications 34.5 (2000): 343-356.
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approved
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#16 by N. J. A. Sloane at Wed Apr 17 10:07:05 EDT 2019
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#15 by Michel Dekking at Wed Apr 17 02:00:05 EDT 2019
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Discussion
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| Wed Apr 17
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| N. J. A. Sloane: Although I agree that the notation { } often denotes a set, in the OEIS {a(n)} is very often used to denote the sequence under discussion.
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#14 by Michel Dekking at Wed Apr 17 01:56:24 EDT 2019
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{(a(n)} )) is a morphic sequence, i.e., a letter-to-letter projection of a fixed point of a morphism. A proof of this is more involved than the proof for the case of the closely related sequence A026609. The reason is that 2 is not the first letter of A026600.
There are several ways to tackle this. We first remark that it suffices to prove that { (a(n)} )) is the image of a fixed point of a morphism by a morphism delta (instead of a letter-to-letter projection), see Corollary 7.7.5 in the book by Allouche and Shallit.
The sequence A026600 is fixed point of the 3-symbol Thue-Morse morphism mu given by mu: 1->123, 2->231, 3->312. Since the first 2 in { (a(n)} )) is at position 2, we consider the 2-block 3-symbol Thue-Morse morphism mu_2 defined on the set of all nine 2-blocks ij by
The frequencies of 0's, 1's and 2's in { (a(n)} )) are 4/13, 5/13 and 4/13.
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proposed
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Discussion
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| Wed Apr 17
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| Michel Dekking: I do not agree with the changes (a(n)) -> {a(n)}. For me anything between {...} is a set. It does not say anywhere in the OEIS Style Sheet that the notation for sequences is {a(n)}. I also turned this back because one instance of (a(n)) was overlooked.
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#13 by Jon E. Schoenfield at Wed Apr 17 01:31:31 EDT 2019
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#12 by Jon E. Schoenfield at Wed Apr 17 01:31:28 EDT 2019
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The frequencies of 0's, 1's and 2's in ( {a(n)) )} are 4/13, 5/13 and 4/13.
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proposed
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