M000146

$$\pi=9365084\arctan\left(\frac{1}{4218932}\right)+11392288\arctan\left(\frac{1}{11612398}\right)-841916\arctan\left(\frac{1}{27089889}\right)+1834296\arctan\left(\frac{1}{34713882}\right)-3914764\arctan\left(\frac{1}{50668324}\right)+612100\arctan\left(\frac{1}{55153444}\right)-4124028\arctan\left(\frac{1}{113014933}\right)+5643648\arctan\left(\frac{1}{226983307}\right)-4326680\arctan\left(\frac{1}{1085592682}\right)+3220256\arctan\left(\frac{2}{4949475989}\right)+1557212\arctan\left(\frac{1}{2701984943}\right)-8469904\arctan\left(\frac{1}{5475957057}\right)+3419160\arctan\left(\frac{1}{6436804193}\right)-1054988\arctan\left(\frac{1}{14033378718}\right)$$
Compact formula9365084[4218932] + 11392288[11612398] - 841916[27089889] + 1834296[34713882] - 3914764[50668324] + 612100[55153444] - 4124028[113014933] + 5643648[226983307] - 4326680[1085592682] + 3220256[4949475989/2] + 1557212[2701984943] - 8469904[5475957057] + 3419160[6436804193] - 1054988[14033378718]
Lehmer's measure1.68879
References
MRW (13Aug06) (full reference coming soon)