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_n s where the n s are Størmer numbers.

Machin-like formulas | Størmer number

James Gregory