M000183

$$\pi=1787516\arctan\left(\frac{1}{1049433}\right)+1311422\arctan\left(\frac{1}{1264557}\right)+621942\arctan\left(\frac{1}{1706203}\right)+1007250\arctan\left(\frac{1}{1984933}\right)-384128\arctan\left(\frac{1}{2478328}\right)-458276\arctan\left(\frac{1}{3449051}\right)-1751858\arctan\left(\frac{1}{18975991}\right)-1233112\arctan\left(\frac{1}{21638297}\right)-374286\arctan\left(\frac{1}{22709274}\right)-343714\arctan\left(\frac{1}{24208144}\right)-503572\arctan\left(\frac{1}{201229582}\right)-865232\arctan\left(\frac{1}{2189376182}\right)$$
Compact formula1787516[1049433] + 1311422[1264557] + 621942[1706203] + 1007250[1984933] - 384128[2478328] - 458276[3449051] - 1751858[18975991] - 1233112[21638297] - 374286[22709274] - 343714[24208144] - 503572[201229582] - 865232[2189376182]
Lehmer's measure1.73115
References
MRW (04Apr97)(12 (integer)-term identity) (full reference coming soon)