M000138

$$\pi=7508496\arctan\left(\frac{1}{5033696}\right)+4130540\arctan\left(\frac{1}{5835807}\right)+7740188\arctan\left(\frac{1}{8519197}\right)-377908\arctan\left(\frac{1}{159358932}\right)+10438692\arctan\left(\frac{1}{162166243}\right)+807332\arctan\left(\frac{1}{213495433}\right)-5956684\arctan\left(\frac{1}{225823278}\right)+511676\arctan\left(\frac{1}{284862638}\right)+190076\arctan\left(\frac{1}{657922943}\right)-8735556\arctan\left(\frac{1}{727507932}\right)+6019008\arctan\left(\frac{2}{1498434239}\right)-8008680\arctan\left(\frac{2}{4417955351}\right)-2398552\arctan\left(\frac{1}{7804016832}\right)+517896\arctan\left(\frac{2}{74522099649}\right)$$
Compact formula7508496[5033696] + 4130540[5835807] + 7740188[8519197] - 377908[159358932] + 10438692[162166243] + 807332[213495433] - 5956684[225823278] + 511676[284862638] + 190076[657922943] - 8735556[727507932] + 6019008[1498434239/2] - 8008680[4417955351/2] - 2398552[7804016832] + 517896[74522099649/2]
Lehmer's measure1.68468
References
MRW (13Aug06) (full reference coming soon)