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We show that the almost sure $\theta$-intermediate dimension of the image ofthe 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 issmaller than that given by directly applying the H\"{o}lder bound forfractional Brownian motion. In particular this establishes the box-countingdimension of these images.

Intermediate dimension of images of sequences under fractional Brownian motion