Can we find a sequence of points in $\mathbb{R}^d$ satisfying the following properties?

Question

I want to choose points $a_1,a_2,a_3,\dots \in \mathbb{R}^d$ such that $|a_n|=n^{1/d}$ and $distance(a_n,a_m)\geq 1$ for all $n,m$. Here $|\cdot|$ is the Euclidean norm.

For example, in $\mathbb{R}$ we can choose $a_n=n$.

Is it possible to choose such a sequence in $\mathbb{R}^d$?