Here's an illustration of an
approach to Π pointed out by Kevin Brown. Define
f(n) as the nearest greater or equal multiple of n-1, then of n-2, etc (yielding OEIS sequence
2491). Then, inverting a result found by Duane Broline and Daniel Loeb, Π = n
2 / f(n).
But as you can see from the comment, the series converges very slowly!
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