M000122

$$\pi=2690\arctan\left(\frac{1}{1023}\right)+3022\arctan\left(\frac{1}{5832}\right)+366\arctan\left(\frac{1}{91093}\right)+366\arctan\left(\frac{1}{103862}\right)-1416\arctan\left(\frac{1}{110443}\right)-1464\arctan\left(\frac{2}{2513489}\right)+1416\arctan\left(\frac{1}{4841182}\right)+332\arctan\left(\frac{1}{6826318}\right)$$
Compact formula2690[1023] + 3022[5832] + 366[91093] + 366[103862] - 1416[110443] - 1464[2513489/2] + 1416[4841182] + 332[6826318]
Lehmer's measure1.65692
References
MRW (***) (full reference coming soon)