M000135

$$\pi=2476996\arctan\left(\frac{1}{1635786}\right)+6307136\arctan\left(\frac{1}{6225244}\right)+6794460\arctan\left(\frac{1}{18975991}\right)+4755324\arctan\left(\frac{1}{22709274}\right)+4745424\arctan\left(\frac{1}{24185182}\right)-117852\arctan\left(\frac{1}{24208144}\right)-7936328\arctan\left(\frac{1}{52630807}\right)-2488948\arctan\left(\frac{1}{54610269}\right)+4983704\arctan\left(\frac{1}{115453918}\right)+344232\arctan\left(\frac{1}{201229582}\right)+3196188\arctan\left(\frac{1}{909140573}\right)+4582148\arctan\left(\frac{1}{2189376182}\right)+2873076\arctan\left(\frac{2}{4532659739}\right)$$
Compact formula2476996[1635786] + 6307136[6225244] + 6794460[18975991] + 4755324[22709274] + 4745424[24185182] - 117852[24208144] - 7936328[52630807] - 2488948[54610269] + 4983704[115453918] + 344232[201229582] + 3196188[909140573] + 4582148[2189376182] + 2873076[4532659739/2]
Lehmer's measure1.68111
References
MRW (26Jun03)(ΒΆΒΆ1.88391) (full reference coming soon)