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Yet another (wrong) construction of π

See more on this concept. Note that the difference between π and this approximation is less than 0.00001, and they are the same in the first 5 digits. You may want to experiment with other values for s, including 413627, 415478, 423379, 450660, 453977, 966976, 969275, 1003999, 1006277, however, some of these cases are equivalent (which ones?).