Machin-like formulae

M000076

$$\pi=3740\arctan\left(\frac{1}{1393}\right)+1288\arctan\left(\frac{1}{3748}\right)+624\arctan\left(\frac{1}{12943}\right)+2120\arctan\left(\frac{1}{32807}\right)+176\arctan\left(\frac{1}{1049433}\right)+1592\arctan\left(\frac{1}{23053977}\right)+1288\arctan\left(\frac{1}{58995773}\right)+1592\arctan\left(\frac{1}{683222322447137}\right)-1592\arctan\left(\frac{1}{550439606940346127492293}\right)$$
Compact formula3740[1393] + 1288[3748] + 624[12943] + 2120[32807] + 176[1049433] + 1592[23053977] + 1288[58995773] + 1592[683222322447137] - 1592[550439606940346127492293]
Lehmer's measure1.60263
References
ASN (28Jul09)(*1.55630, *1.66383 - both 3-digit) (full reference coming soon)
Contributing