-4
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3, 3, 5, 4, 4, 3, 5, 5, 4, 3

How did I get those numbers and how do I get more that fit the pattern?

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6
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the pattern comes from:

the letter count of the names of the numbers 1 to 10

Because

one has 3 letters, two has 3 letters, and so on.

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