Working over the alphabet {1,2,3}, start with a(1) = 1; then a(n+1) is made by inserting a letter into a(n) at the rightmost possible position which makes a squarefree word (and the smallest letter if multiple letters are possible at that place).

A332603

Working over the alphabet {1,2,3}, start with a(1) = 1; then a(n+1) is made by inserting a letter into a(n) at the rightmost possible position which makes a squarefree word (and the smallest letter if multiple letters are possible at that place).