M000009124

$$\pi=-8\arctan\left(\frac{1}{4}\right)+16\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{8}\right)+8\arctan\left(\frac{1}{21}\right)$$
Compact formula- 8[4] + 16[5] + 4[7] + 8[8] + 8[21]
Lehmer's measure6.13854