M000000305

$$\pi=48\arctan\left(\frac{1}{15}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{580}\right)-16\arctan\left(\frac{1}{1710}\right)$$
Compact formula48[15] - 4[239] - 16[580] - 16[1710]
Lehmer's measure1.94190
References
Castellanos, Dario. The ubuquitous π, Mathematics Magazine 61, 1988. [DOI: 10.1080/0025570X.1988.11977350]