M000147

$$\pi=2378340\arctan\left(\frac{1}{2484568}\right)+7828660\arctan\left(\frac{1}{4218932}\right)+4951776\arctan\left(\frac{1}{11612398}\right)-2227876\arctan\left(\frac{1}{34713882}\right)-229816\arctan\left(\frac{1}{55153444}\right)-4124028\arctan\left(\frac{1}{113014933}\right)+1581476\arctan\left(\frac{1}{226983307}\right)+841916\arctan\left(\frac{2}{821598989}\right)-1106424\arctan\left(\frac{1}{1085592682}\right)-1663044\arctan\left(\frac{1}{2701984943}\right)-3713224\arctan\left(\frac{1}{5475957057}\right)+3419160\arctan\left(\frac{1}{6436804193}\right)-1054988\arctan\left(\frac{1}{14033378718}\right)+841916\arctan\left(\frac{1}{137499481467279382}\right)-841916\arctan\left(\frac{1}{1196602956151217979146736}\right)$$
Compact formula2378340[2484568] + 7828660[4218932] + 4951776[11612398] - 2227876[34713882] - 229816[55153444] - 4124028[113014933] + 1581476[226983307] + 841916[821598989/2] - 1106424[1085592682] - 1663044[2701984943] - 3713224[5475957057] + 3419160[6436804193] - 1054988[14033378718] + 841916[137499481467279382] - 841916[1196602956151217979146736]
Lehmer's measure1.69034
References
ASN (5Jan10)(*1.70886, ΒΆΒΆ1.88278) (full reference coming soon)