M000000049

$$\pi=\frac{62324}{3}\arctan\left(\frac{1}{6807}\right)+\frac{19352}{3}\arctan\left(\frac{2}{200779}\right)+2324\arctan\left(\frac{2}{362619}\right)+\frac{3232}{3}\arctan\left(\frac{1}{623098}\right)+4424\arctan\left(\frac{1}{734557}\right)+7528\arctan\left(\frac{1}{2634273}\right)+\frac{6424}{3}\arctan\left(\frac{1}{6826318}\right)+9900\arctan\left(\frac{1}{7626068}\right)+\frac{21548}{3}\arctan\left(\frac{1}{21072618}\right)$$
Compact formula62324/3[6807] + 19352/3[200779/2] + 2324[362619/2] + 3232/3[623098] + 4424[734557] + 7528[2634273] + 6424/3[6826318] + 9900[7626068] + 21548/3[21072618]
Lehmer's measure1.57796
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 15 October 2009.]