M000017185

$$\pi=20\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{3}{79}\right)$$
Compact formula20[7] + 8[79/3]
Lehmer's measure1.88726
References
Euler, Leonhard. Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae, Nova acta academiae scientiarum Petropolitinae 11, 133–149, 1798. [Presented in 1779. Republished in Opera omnia, I.16, 1-20.]

Vega, Jurij. Thesaurus Logarithmorum Completus, 1794. [Formula used on page 633.]