M000155

$$\pi=1093868\arctan\left(\frac{2}{1230349}\right)+2225728\arctan\left(\frac{1}{2298668}\right)+907296\arctan\left(\frac{1}{5033696}\right)+1564896\arctan\left(\frac{1}{5835807}\right)-708832\arctan\left(\frac{1}{8519197}\right)+377908\arctan\left(\frac{2}{42557349}\right)+609268\arctan\left(\frac{1}{168623905}\right)+1398468\arctan\left(\frac{1}{225823278}\right)+511676\arctan\left(\frac{1}{227661182}\right)-517896\arctan\left(\frac{2}{1091236511}\right)+707972\arctan\left(\frac{1}{657922943}\right)-497352\arctan\left(\frac{1}{7804016832}\right)+895804\arctan\left(\frac{1}{8120692247}\right)$$
Compact formula1093868[1230349/2] + 2225728[2298668] + 907296[5033696] + 1564896[5835807] - 708832[8519197] + 377908[42557349/2] + 609268[168623905] + 1398468[225823278] + 511676[227661182] - 517896[1091236511/2] + 707972[657922943] - 497352[7804016832] + 895804[8120692247]
Lehmer's measure1.69847
References
MRW (13Aug06) (full reference coming soon)