M000232

$$\pi=\frac{6416711464}{5}\arctan\left(\frac{1}{1832735843}\right)+\frac{35781768804}{5}\arctan\left(\frac{2}{4417955351}\right)+4197060628\arctan\left(\frac{1}{3411640081}\right)\frac{-47668784428}{5}\arctan\left(\frac{1}{5475957057}\right)-397970320\arctan\left(\frac{1}{6852438287}\right)\frac{-16651121632}{5}\arctan\left(\frac{1}{8120692247}\right)+\frac{27457193276}{5}\arctan\left(\frac{1}{12139595709}\right)+\frac{8376432024}{5}\arctan\left(\frac{1}{50211838227}\right)-3512186652\arctan\left(\frac{2}{112899039159}\right)\frac{-19339220952}{5}\arctan\left(\frac{2}{115004793075}\right)\frac{-34528816184}{5}\arctan\left(\frac{1}{113201494333}\right)\frac{-66270439004}{5}\arctan\left(\frac{1}{120563046313}\right)\frac{-18470439948}{5}\arctan\left(\frac{1}{396865168415}\right)\frac{-2797279752}{5}\arctan\left(\frac{1}{460973867151}\right)+5171141060\arctan\left(\frac{1}{831235366457}\right)\frac{-51865064}{5}\arctan\left(\frac{1}{13483667897487}\right)\frac{-14482565616}{5}\arctan\left(\frac{1}{15962244871097}\right)\frac{-14277463172}{5}\arctan\left(\frac{2}{43777069138111}\right)\frac{-5274932512}{5}\arctan\left(\frac{1}{169838669284032}\right)\frac{-15876358212}{5}\arctan\left(\frac{1}{180481359172943}\right)$$
Compact formula6416711464/5[1832735843] + 35781768804/5[4417955351/2] + 4197060628[3411640081] - 47668784428/5[5475957057] - 397970320[6852438287] - 16651121632/5[8120692247] + 27457193276/5[12139595709] + 8376432024/5[50211838227] - 3512186652[112899039159/2] - 19339220952/5[115004793075/2] - 34528816184/5[113201494333] - 66270439004/5[120563046313] - 18470439948/5[396865168415] - 2797279752/5[460973867151] + 5171141060[831235366457] - 51865064/5[13483667897487] - 14482565616/5[15962244871097] - 14277463172/5[43777069138111/2] - 5274932512/5[169838669284032] - 15876358212/5[180481359172943]
Lehmer's measure1.80754
References
MRW (10Aug06) (full reference coming soon)