Machin-like formulae

M000481

$$\pi=2476996\arctan\left(\frac{1}{1635786}\right)+2873076\arctan\left(\frac{1}{3014557}\right)+3434060\arctan\left(\frac{1}{6225244}\right)+3921384\arctan\left(\frac{1}{18975991}\right)+1882248\arctan\left(\frac{1}{22709274}\right)-1000728\arctan\left(\frac{1}{24185182}\right)-117852\arctan\left(\frac{1}{24208144}\right)-5063252\arctan\left(\frac{1}{52630807}\right)-2488948\arctan\left(\frac{1}{54610269}\right)+2110628\arctan\left(\frac{1}{115453918}\right)+344232\arctan\left(\frac{1}{201229582}\right)+323112\arctan\left(\frac{1}{909140573}\right)+1709072\arctan\left(\frac{1}{2189376182}\right)$$
Compact formula2476996[1635786] + 2873076[3014557] + 3434060[6225244] + 3921384[18975991] + 1882248[22709274] - 1000728[24185182] - 117852[24208144] - 5063252[52630807] - 2488948[54610269] + 2110628[115453918] + 344232[201229582] + 323112[909140573] + 1709072[2189376182]
Lehmer's measure1.72856
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

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