M000057

$$\pi=2324\arctan\left(\frac{1}{1252}\right)+3056\arctan\left(\frac{1}{2855}\right)+1064\arctan\left(\frac{1}{5832}\right)+1464\arctan\left(\frac{1}{58898}\right)+780\arctan\left(\frac{1}{110443}\right)+2148\arctan\left(\frac{1}{4841182}\right)+1064\arctan\left(\frac{1}{6826318}\right)$$
Compact formula2324[1252] + 3056[2855] + 1064[5832] + 1464[58898] + 780[110443] + 2148[4841182] + 1064[6826318]
Lehmer's measure1.58160
References
HCL (19Jul95)(*1.55905) (full reference coming soon)