Formula for the sequence $4, 10, 16, 22, 25, 34 ,\ldots$

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Given the sequence $4, 10, 16, 22, 25, 34,\ldots$ how can I derive a formula for it?

Hint: Those numbers appear when I multiply the results of a given function in ascending order.

This function is:

$$f(n) = 3n + 2$$ for $n=0,1,2,3,4, ... $

For instance, if $f(n) = 2, 5 , 8 , 11, 14, 17, 20, 23,\ldots$ then I create the sequence I am asking for: $2\times2$, $2\times5$, $2\times8$, $2\times11$ and then I take $5\times5$ because it is bigger than $2\times11$ and smaller than $2\times14$.

Is there anyway I can derive a formula to it?