A number t_x = tan^(-1)(1/x) = cot^(-1) x, where x is an integer or rational number, tan^(-1) x is the inverse tangent, and cot^(-1) x is the inverse cotangent. Gregory numbers arise in the determination of Machin-like formulas. Every Gregory number t_x can be expressed uniquely as a linear combination of t_ns where the ns are Størmer numbers.
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