M000008

$$\pi=5380\arctan\left(\frac{1}{1712}\right)-88\arctan\left(\frac{1}{103697}\right)-48\arctan\left(\frac{2}{2513489}\right)+68\arctan\left(\frac{2}{2927521}\right)-332\arctan\left(\frac{1}{4900493}\right)-664\arctan\left(\frac{1}{39202018}\right)-1328\arctan\left(\frac{1}{313612292}\right)-2656\arctan\left(\frac{1}{2508890632}\right)-88\arctan\left(\frac{2}{18280007883}\right)$$
Compact formula5380[1712] - 88[103697] - 48[2513489/2] + 68[2927521/2] - 332[4900493] - 664[39202018] - 1328[313612292] - 2656[2508890632] - 88[18280007883/2]
Lehmer's measure1.44042
References
ASN (2007-8)(*1.26579) (full reference coming soon)