M000003511
$$\pi=-16\arctan\left(\frac{1}{3}\right)+32\arctan\left(\frac{1}{5}\right)+32\arctan\left(\frac{1}{21}\right)+16\arctan\left(\frac{1}{23}\right)-16\arctan\left(\frac{1}{38}\right)+16\arctan\left(\frac{1}{83}\right)-8\arctan\left(\frac{1}{478}\right)+4\arctan\left(\frac{1}{54608393}\right)$$