Gregory Number

A number

$$t_x=\tan^{-1}({\textstyle{1\over x}})=\cot^{-1} x,$$

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 sum of $t_n$s where the $n$s are Størmer Numbers.

References

Conway, J. H. and Guy, R. K. ``Gregory's Numbers'' In The Book of Numbers. New York: Springer-Verlag, pp. 241-242, 1996.