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How does this sequence of integers continue?

4 5 8 8 9 9 12 13

Not too difficult I think.

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Answer:

13.

Explanation:

ONE = three letters, +1 = 4
TWO = three letters, +2 = 5
THREE = five letters, +3 = 8

etc.

NINE = four letters, +9 = 13

Note

This sequence has a name (here starting at $0$): https://oeis.org/A095945

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