M000210

$$\pi=227800256\arctan\left(\frac{1}{227661182}\right)+187578340\arctan\left(\frac{1}{244653118}\right)-80034080\arctan\left(\frac{1}{284862638}\right)+258052932\arctan\left(\frac{1}{307885245}\right)+173889680\arctan\left(\frac{1}{355671793}\right)+43912224\arctan\left(\frac{1}{403478642}\right)+197214844\arctan\left(\frac{1}{403916362}\right)-115624128\arctan\left(\frac{2}{1049730289}\right)-42342444\arctan\left(\frac{1}{727507932}\right)+27265628\arctan\left(\frac{1}{15234751332}\right)+115983700\arctan\left(\frac{2}{58632782131}\right)+197367692\arctan\left(\frac{2}{74522099649}\right)-89538596\arctan\left(\frac{1}{37956026467}\right)+6107352\arctan\left(\frac{1}{106334643058}\right)+86556660\arctan\left(\frac{1}{134520516108}\right)+27077796\arctan\left(\frac{1}{138873731225}\right)+61468536\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula227800256[227661182] + 187578340[244653118] - 80034080[284862638] + 258052932[307885245] + 173889680[355671793] + 43912224[403478642] + 197214844[403916362] - 115624128[1049730289/2] - 42342444[727507932] + 27265628[15234751332] + 115983700[58632782131/2] + 197367692[74522099649/2] - 89538596[37956026467] + 6107352[106334643058] + 86556660[134520516108] + 27077796[138873731225] + 61468536[169838669284032]
Lehmer's measure1.77524
References
MRW (11Aug06) (full reference coming soon)