The Flint Hills series is the series S_1 = sum_(n = 1)^∞ (csc^2 n)/n^3 (Pickover 2002, p. 59). It is not known if this series converges, since csc^2 n can have sporadic large values. The plots above show its behavior up to n = 10^4. The positive integer values of n giving incrementally largest values of left bracketing bar csc n right bracketing bar are given by 1, 3, 22, 333, 355, 103993, ... (OEIS A046947), which are precisely the numerators of the convergents of π, corresponding to the values 1.1884, 7.08617, 112.978, 113.364, 33173.7, ....

Cookson Hills series | irrationality measure | tanc function