M000426

$$\pi=28\arctan\left(\frac{1}{10}\right)+8\arctan\left(\frac{1}{50}\right)+16\arctan\left(\frac{1}{100}\right)+4\arctan\left(\frac{1}{682}\right)+16\arctan\left(\frac{1}{1000}\right)+12\arctan\left(\frac{1}{1303}\right)-16\arctan\left(\frac{1}{90109}\right)$$
Compact formula28[10] + 8[50] + 16[100] + 4[682] + 16[1000] + 12[1303] - 16[90109]
Lehmer's measure3.29766
References
Wrench Jr., J. W. On the derivation of arctangent equalities, The American Mathematical Monthly 45, 108–109, 1938. [DOI: 10.2307/2304280]