M000249

$$\pi=3282161352\arctan\left(\frac{1}{1454097393}\right)+1796754096\arctan\left(\frac{2}{5493779561}\right)-262541244\arctan\left(\frac{1}{4038832337}\right)-48258860\arctan\left(\frac{1}{4474115807}\right)-1957462428\arctan\left(\frac{1}{6608082112}\right)+2390049812\arctan\left(\frac{2}{16758521543}\right)+2782654088\arctan\left(\frac{2}{36523075989}\right)+229449136\arctan\left(\frac{1}{18710140581}\right)+2406487236\arctan\left(\frac{1}{29546599818}\right)+853709636\arctan\left(\frac{1}{38185029043}\right)+1507140800\arctan\left(\frac{2}{112899039159}\right)+3546521480\arctan\left(\frac{1}{193271326807}\right)+2603175604\arctan\left(\frac{1}{265542904947}\right)-2494757392\arctan\left(\frac{1}{378137211957}\right)+685716688\arctan\left(\frac{1}{3737240479718}\right)+2947084480\arctan\left(\frac{1}{8256835333313}\right)-299718500\arctan\left(\frac{1}{10041983931693}\right)-2819401792\arctan\left(\frac{1}{11830545643782}\right)+4324905012\arctan\left(\frac{1}{46150510628682}\right)+1353663992\arctan\left(\frac{1}{69971515635443}\right)$$
Compact formula3282161352[1454097393] + 1796754096[5493779561/2] - 262541244[4038832337] - 48258860[4474115807] - 1957462428[6608082112] + 2390049812[16758521543/2] + 2782654088[36523075989/2] + 229449136[18710140581] + 2406487236[29546599818] + 853709636[38185029043] + 1507140800[112899039159/2] + 3546521480[193271326807] + 2603175604[265542904947] - 2494757392[378137211957] + 685716688[3737240479718] + 2947084480[8256835333313] - 299718500[10041983931693] - 2819401792[11830545643782] + 4324905012[46150510628682] + 1353663992[69971515635443]
Lehmer's measure1.82151
References
MRW (10Aug06) (full reference coming soon)