M000125

$$\pi=1288\arctan\left(\frac{1}{577}\right)+304\arctan\left(\frac{1}{682}\right)+556\arctan\left(\frac{1}{1393}\right)+624\arctan\left(\frac{1}{12943}\right)+528\arctan\left(\frac{1}{32807}\right)+176\arctan\left(\frac{1}{1049433}\right)$$
Compact formula1288[577] + 304[682] + 556[1393] + 624[12943] + 528[32807] + 176[1049433]
Lehmer's measure1.66383
References
ARNDT (1993) (full reference coming soon)