M000384

$$\pi=\frac{224}{3}\arctan\left(\frac{1}{23}\right)\frac{-4}{3}\arctan\left(\frac{1}{182}\right)\frac{-100}{3}\arctan\left(\frac{1}{500}\right)\frac{-80}{3}\arctan\left(\frac{1}{924}\right)+\frac{20}{3}\arctan\left(\frac{1}{99557}\right)+\frac{40}{3}\arctan\left(\frac{1}{298307}\right)$$
Compact formula224/3[23] - 4/3[182] - 100/3[500] - 80/3[924] + 20/3[99557] + 40/3[298307]
Lehmer's measure2.26726
References
Wrench Jr., J. W. On the derivation of arctangent equalities, The American Mathematical Monthly 45, 108–109, 1938. [DOI: 10.2307/2304280]