What is this pattern?

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I have a pattern of numbers from some simulation that I'm trying to piece backwards into some sort of formula. All I can see right now is that they maybe have to do with integrals? The numbers (which may be a decimal or so out, as this is approximated from simulation) and their associated values are: $$2 - 125$$ $$3 - 142.6$$ $$4 - 166.7$$ $$5 - 200$$

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2 Answers

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For a general $n$, we have $n - \frac{1000}{10-n}$

See that $\frac{1000}{10-2}=\frac{1000}{8}=125$ for example.

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There are too few values here to say much, but there's a pretty good fit to $112.5 + 2.9 n^{2.116}$.

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