An interesting sequence,Look and say sequnce

Question

Why in this sequence $$1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221$$

333 never appears? It is a Look and say sequence.

Answer 1

If a sequence $abc$ appears in some term, then either the previous term had $a$ consecutive occurrences of $b$, or $b$ consecutive occurrences of $c$. In particular, if $aaa$ occurs, the previous term has $a$ consectutive $a$s. So for $333$ to occur, the previous term has three consecutive $3$s, so a $333$ within.

Answer 2

Say $3332$ occurs in a term. Then the previous term must contain $333222$, and the term prior to that would have to contain $33322222$ making the next term $3352$ rather than $333222$.

$333222$ is not achievable, and so neither is $3332$.