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A332604
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Limiting word over the alphabet {1,2,3} defined by the process in A332603, or, in case that process terminates, the final term in A332603.
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1
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1, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 2, 1, 3, 1, 2, 3, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 2, 1, 2, 3, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 2, 1, 3
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OFFSET
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1,2
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COMMENTS
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Grytczuk et al. (2020) conjecture that the process in A332603 never terminates, and report that they have computed the first 5000 terms of the limiting word.
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LINKS
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Jaroslaw Grytczuk, Hubert Kordulewski, Artur Niewiadomski, Extremal Square-Free Words, Electronic J. Combinatorics, 27 (1), 2020, #1.48.
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MATHEMATICA
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sqfQ[str_] := StringFreeQ[str, x__ ~~ x__]; ext[s_] := Catch@ Block[{t}, Do[ If[sqfQ[t = StringInsert[s, e, -p]], Throw@ t], {p, StringLength[s] + 1}, {e, {"1", "2", "3"} } ]]; a[1]=1; a[n_] := a[n] = ToExpression@ ext@ ToString@ a[n-1]; IntegerDigits@ a[88] (* Giovanni Resta, Mar 09 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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