M000036

$$\pi=2324\arctan\left(\frac{1}{1252}\right)+3056\arctan\left(\frac{1}{5593}\right)+4120\arctan\left(\frac{1}{5832}\right)+1464\arctan\left(\frac{1}{58898}\right)+780\arctan\left(\frac{1}{110443}\right)+2148\arctan\left(\frac{1}{4841182}\right)+1064\arctan\left(\frac{1}{6826318}\right)$$
Compact formula2324[1252] + 3056[5593] + 4120[5832] + 1464[58898] + 780[110443] + 2148[4841182] + 1064[6826318]
Lehmer's measure1.55905
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

MRW (06Dec94)(*1.56846, ΒΆΒΆ1.97950) (full reference coming soon)