M000211

$$\pi=\frac{453957268}{3}\arctan\left(\frac{1}{127120947}\right)+\frac{139836916}{3}\arctan\left(\frac{2}{322564791}\right)+\frac{517783072}{3}\arctan\left(\frac{1}{201229582}\right)\frac{-103840088}{3}\arctan\left(\frac{1}{274576229}\right)+\frac{461579620}{3}\arctan\left(\frac{1}{284862638}\right)+14261956\arctan\left(\frac{1}{299252491}\right)+\frac{404724440}{3}\arctan\left(\frac{2}{826867939}\right)-46329268\arctan\left(\frac{2}{3472598789}\right)+129874672\arctan\left(\frac{1}{3866973557}\right)+\frac{431696812}{3}\arctan\left(\frac{1}{7427844818}\right)-39014080\arctan\left(\frac{1}{12601326140}\right)\frac{-312803384}{3}\arctan\left(\frac{1}{29942196097}\right)\frac{-14995472}{3}\arctan\left(\frac{2}{75525552427}\right)\frac{-531890852}{3}\arctan\left(\frac{1}{64506738863}\right)\frac{-63257576}{3}\arctan\left(\frac{1}{118034929852}\right)\frac{-224661344}{3}\arctan\left(\frac{2}{1087840667761}\right)\frac{-207007156}{3}\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula453957268/3[127120947] + 139836916/3[322564791/2] + 517783072/3[201229582] - 103840088/3[274576229] + 461579620/3[284862638] + 14261956[299252491] + 404724440/3[826867939/2] - 46329268[3472598789/2] + 129874672[3866973557] + 431696812/3[7427844818] - 39014080[12601326140] - 312803384/3[29942196097] - 14995472/3[75525552427/2] - 531890852/3[64506738863] - 63257576/3[118034929852] - 224661344/3[1087840667761/2] - 207007156/3[169838669284032]
Lehmer's measure1.77763
References
ASN (13Jan10) (full reference coming soon)