M000197

$$\pi=195782408\arctan\left(\frac{2}{322564791}\right)+289300084\arctan\left(\frac{1}{201229582}\right)+156008860\arctan\left(\frac{1}{284862638}\right)+32464376\arctan\left(\frac{1}{546365045}\right)-87856852\arctan\left(\frac{1}{778401733}\right)-60591224\arctan\left(\frac{1}{1514342682}\right)-30640352\arctan\left(\frac{2}{4204410541}\right)-145862396\arctan\left(\frac{1}{3866973557}\right)+13864892\arctan\left(\frac{2}{11352069609}\right)+433248352\arctan\left(\frac{1}{6421564557}\right)-66584416\arctan\left(\frac{1}{7427844818}\right)+254159924\arctan\left(\frac{1}{7959681215}\right)+42052804\arctan\left(\frac{2}{75525552427}\right)-354454708\arctan\left(\frac{2}{108928448489}\right)+58429812\arctan\left(\frac{1}{118034929852}\right)+74282988\arctan\left(\frac{2}{1087840667761}\right)-202483572\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula195782408[322564791/2] + 289300084[201229582] + 156008860[284862638] + 32464376[546365045] - 87856852[778401733] - 60591224[1514342682] - 30640352[4204410541/2] - 145862396[3866973557] + 13864892[11352069609/2] + 433248352[6421564557] - 66584416[7427844818] + 254159924[7959681215] + 42052804[75525552427/2] - 354454708[108928448489/2] + 58429812[118034929852] + 74282988[1087840667761/2] - 202483572[169838669284032]
Lehmer's measure1.74824
References
ASN (21Dec09)(ΒΆΒΆ1.89581) (full reference coming soon)