  We show that the almost sure $\theta$-intermediate dimension of the image of
the set $F_p =\{0, 1,\frac{1}{2^p},\frac{1}{3^p},\ldots\}$ under index-$h$
fractional Brownian motion is $\frac{\theta}{ph+\theta}$, a value that is
smaller than that given by directly applying the H\"{o}lder bound for
fractional Brownian motion. In particular this establishes the box-counting
dimension of these images.
