In this paper we present a two-term Machin-like formula for pi \[\frac{ \pi}{ 4} = 2^{ k - 1}\arctan\left(\frac{ 1}{ u_1}\right) + \arctan\left(\frac{ 1}{ u_2}\right)\] with small Lehmer's measure $e \approx 0.245319$ and describe iteration procedure for simplified determination of the required rational number $u_2$ at $k = 27$ and $u_1 = 85445659$. With these results we obtained a formula that has no irrational numbers involved in computation and provides $16$ digits of pi at each increment by one of the summation terms. This is the smallest Lehmer's measure ever reported for the Machin-like formulas for pi.
Categories: math.GM