We consider sequential procedures for obtaining confidence intervals of prescribed length and confidence coefficient for the mean of a normal distribution with known variance. A procedure achieving these aims is called optimum if it minimizes the least upper bound (with respect to the mean) of the expected number of observations. The result proved is that the usual nonsequential procedure is optimum.
"Sequential Confidence Intervals for the Mean of a Normal Distribution with Known Variance." Ann. Math. Statist. 18 (3) 427 - 433, September, 1947. https://doi.org/10.1214/aoms/1177730389