M000143

$$\pi=10438408\arctan\left(\frac{1}{3014557}\right)-1073324\arctan\left(\frac{2}{16840821}\right)-1239128\arctan\left(\frac{1}{24208144}\right)+184140\arctan\left(\frac{1}{54610269}\right)-1310044\arctan\left(\frac{1}{63199427}\right)-10283920\arctan\left(\frac{1}{100656977}\right)-4169040\arctan\left(\frac{1}{115453918}\right)+1166952\arctan\left(\frac{2}{322564791}\right)+4516132\arctan\left(\frac{1}{385231007}\right)-1355720\arctan\left(\frac{1}{1304967682}\right)-3921384\arctan\left(\frac{2}{4532659739}\right)-7681544\arctan\left(\frac{2}{4949475989}\right)+2115052\arctan\left(\frac{1}{18986886768}\right)+4327364\arctan\left(\frac{2}{520629831511}\right)$$
Compact formula10438408[3014557] - 1073324[16840821/2] - 1239128[24208144] + 184140[54610269] - 1310044[63199427] - 10283920[100656977] - 4169040[115453918] + 1166952[322564791/2] + 4516132[385231007] - 1355720[1304967682] - 3921384[4532659739/2] - 7681544[4949475989/2] + 2115052[18986886768] + 4327364[520629831511/2]
Lehmer's measure1.68684
References
ASN (27May10)(ΒΆΒΆ1.87150) (full reference coming soon)