M000000076

$$\pi=3740\arctan\left(\frac{1}{1393}\right)+1288\arctan\left(\frac{1}{3748}\right)+624\arctan\left(\frac{1}{12943}\right)+2120\arctan\left(\frac{1}{32807}\right)+176\arctan\left(\frac{1}{1049433}\right)+1592\arctan\left(\frac{1}{23053977}\right)+1288\arctan\left(\frac{1}{58995773}\right)+1592\arctan\left(\frac{1}{683222322447137}\right)-1592\arctan\left(\frac{1}{550439606940346127492293}\right)$$
Compact formula3740[1393] + 1288[3748] + 624[12943] + 2120[32807] + 176[1049433] + 1592[23053977] + 1288[58995773] + 1592[683222322447137] - 1592[550439606940346127492293]
Lehmer's measure1.60263
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 28 July 2009.]