M000000428

$$\pi=24\arctan\left(\frac{1}{10}\right)+12\arctan\left(\frac{1}{18}\right)+8\arctan\left(\frac{1}{100}\right)+8\arctan\left(\frac{1}{307}\right)-12\arctan\left(\frac{1}{515}\right)+8\arctan\left(\frac{1}{9901}\right)$$
Compact formula24[10] + 12[18] + 8[100] + 8[307] - 12[515] + 8[9901]
Lehmer's measure3.31773
References
Castellanos, Dario. The ubuquitous π, Mathematics Magazine 61, 1988. [DOI: 10.1080/0025570X.1988.11977350]