M000038

$$\pi=2324\arctan\left(\frac{1}{1023}\right)+732\arctan\left(\frac{1}{1710}\right)+2656\arctan\left(\frac{1}{5832}\right)-1416\arctan\left(\frac{1}{105218}\right)-48\arctan\left(\frac{2}{2513489}\right)+332\arctan\left(\frac{1}{6826318}\right)-1416\arctan\left(\frac{1}{7167807}\right)$$
Compact formula2324[1023] + 732[1710] + 2656[5832] - 1416[105218] - 48[2513489/2] + 332[6826318] - 1416[7167807]
Lehmer's measure1.56236
References
MRW (23Sep04) (full reference coming soon)