The Cookson Hills series is the series similar to the Flint Hills series, but with numerator sec^2 n instead of csc^2 n: S_2 = sum_(n = 1)^∞ (sec^2 n)/n^3 (Pickover 2002, p. 268). It is not known if this series converges since sec^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 sec n right bracketing bar are given by 1, 2, 5, 8, 11, 344, 699, 1054, 1409, 1764, 2119, ... (OEIS A004112), corresponding to the values 1.85082, 2.403, 3.52532, 6.87285, 225.953, 227.503, ....
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