M000395

$$\pi=20\arctan\left(\frac{1}{8}\right)+8\arctan\left(\frac{1}{18}\right)+12\arctan\left(\frac{1}{57}\right)$$
Compact formula20[8] + 8[18] + 12[57]
Lehmer's measure2.47346
References
SCHELLBACH (1832) (full reference coming soon)