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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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%I #15 Mar 09 2020 13:01:41

%S 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,

%T 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,

%U 3,2,3,1,2,1,3,1,2,3,1,3,2,1,2,3,1,2,1,3

%N 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.

%C 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.

%H Jaroslaw Grytczuk, Hubert Kordulewski, Artur Niewiadomski, <a href="https://doi.org/10.37236/9264">Extremal Square-Free Words</a>, Electronic J. Combinatorics, 27 (1), 2020, #1.48.

%t 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 *)

%Y Cf. A332603.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 07 2020

%E More terms from _Giovanni Resta_, Mar 09 2020