Hard Logic Sequence Puzzle

Complete the following series. It.s very logical:

1, 4, 5, 6, 7, 9, 11, __?




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👉 I am a 7 letter word.
👉 I like mornings
👉 If you remove my 1st letter you can drink me
👉 If you remove my 1st & 2nd letters 👉 you may not like me
👉 If you remove my last letter, you will see me on television
👉Answer is really very interesting
Let us see who solves this....

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Amazing Facts

Challenging

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