Machin-like formulae

M000484

$$\pi=20136504\arctan\left(\frac{1}{20942043}\right)+6184012\arctan\left(\frac{1}{22709274}\right)+25914536\arctan\left(\frac{1}{24185182}\right)+2755224\arctan\left(\frac{1}{24208144}\right)-3921384\arctan\left(\frac{1}{27005643}\right)+6295184\arctan\left(\frac{1}{54610269}\right)+17659508\arctan\left(\frac{1}{63199427}\right)+6213576\arctan\left(\frac{1}{100656977}\right)+26635940\arctan\left(\frac{1}{115453918}\right)+18707816\arctan\left(\frac{1}{116428593}\right)-3181072\arctan\left(\frac{1}{201229582}\right)+23984920\arctan\left(\frac{1}{909140573}\right)+19275020\arctan\left(\frac{1}{2189376182}\right)+7920628\arctan\left(\frac{1}{18986886768}\right)+5350072\arctan\left(\frac{1}{250645741818}\right)$$
Compact formula20136504[20942043] + 6184012[22709274] + 25914536[24185182] + 2755224[24208144] - 3921384[27005643] + 6295184[54610269] + 17659508[63199427] + 6213576[100656977] + 26635940[115453918] + 18707816[116428593] - 3181072[201229582] + 23984920[909140573] + 19275020[2189376182] + 7920628[18986886768] + 5350072[250645741818]
Lehmer's measure1.83249
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

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