M000000035

$$\pi=1288\arctan\left(\frac{1}{577}\right)+1164\arctan\left(\frac{1}{1393}\right)+624\arctan\left(\frac{1}{12943}\right)+832\arctan\left(\frac{1}{32807}\right)+176\arctan\left(\frac{1}{1049433}\right)+304\arctan\left(\frac{1}{23053977}\right)+304\arctan\left(\frac{1}{683222322447137}\right)+304\arctan\left(\frac{1}{550439606940346127492293}\right)$$
Compact formula1288[577] + 1164[1393] + 624[12943] + 832[32807] + 176[1049433] + 304[23053977] + 304[683222322447137] + 304[550439606940346127492293]
Lehmer's measure1.55629
References
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 Amrik Singh Nimbran on 27 July 2009.]