Key points are not available for this paper at this time.
Lawrence Joseph, David B. Wolfson, Roxane Du Berger, Sample Size Calculations for Binomial Proportions via Highest Posterior Density Intervals, Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 44, No. 2 (1995), pp. 143-154
Joseph et al. (Sun,) studied this question.