M000003510
$$\pi=16\arctan\left(\frac{1}{5}\right)+16\arctan\left(\frac{1}{21}\right)-16\arctan\left(\frac{1}{27}\right)-16\arctan\left(\frac{1}{86}\right)-4\arctan\left(\frac{1}{252}\right)+16\arctan\left(\frac{1}{939}\right)-4\arctan\left(\frac{1}{4633}\right)-16\arctan\left(\frac{1}{1764383}\right)$$