M000000281

$$\pi=68\arctan\left(\frac{1}{26}\right)+20\arctan\left(\frac{1}{38}\right)+12\arctan\left(\frac{1}{2682}\right)-28\arctan\left(\frac{1}{8827}\right)$$
Compact formula68[26] + 20[38] + 12[2682] - 28[8827]
Lehmer's measure1.88483
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81(490), 120–121, 1997. [DOI: 10.2307/3618793]

Wetherfield, Michael Roby and Chien-Lih, Hwang. Computing pi: Lists of Machin-type (inverse cotangent) identities for pi/4, [Online; accessed 04-February-2024], 2013. [web.archive.org/web/20240204042153/http] [Found by HCL on 28 September 1993.]