Why in this sequence $$1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221$$
333 never appears? It is a Look and say sequence.
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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.