Find the Next No.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211




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There is an exact a week gap between Christmas and New Year. Hence, It is obvious that the new year that comes right after Christmas comes on the same day of the week.

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.