  This paper studies the logarithmic moments of the smallest denominator of all
rationals in a shrinking interval with random center. Convergence follows from
the more general results in [arXiv:2310.11251, Bull. Lond. Math. Soc., to
appear], and the key point of this note is the derivation of explicit formulas
for the moments of the limit distribution in dimension one. This answers
questions raised by Meiss and Sander in their numerical study of minimal
resonance orders for torus maps with random rotation vectors
[arXiv:2310.11600].
