A332604 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.

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

Offset: 1

Author

N. J. A. Sloane, Mar 07 2020

Keywords

• nonn

Comments

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.

Links

• Jaroslaw Grytczuk, Hubert Kordulewski, Artur Niewiadomski, Extremal Square-Free Words, Electronic J. Combinatorics, 27 (1), 2020, #1.48.

Crossrefs

Cf. A332603.

Programs

Mathematica

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 *)

Extensions

More terms from Giovanni Resta, Mar 09 2020