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

1,2

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

Table of n, a(n) for n=1..88.

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

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 *)

Crossrefs

Cf. A332603.

Sequence in context: A105497 A255809 A382528 * A132662 A279782 A358921

Adjacent sequences: A332601 A332602 A332603 * A332605 A332606 A332607

Keyword

nonn

Author

N. J. A. Sloane, Mar 07 2020

Extensions

More terms from Giovanni Resta, Mar 09 2020

Status

approved