  This note presents an example of an increasing sequence
$(\lambda_l)_{l=1}^\infty$ such that the maximal operators associated to
normalized discrete spherical convolution averages \[ \sup_{l\geq
1}\frac{1}{r(\lambda_l)}\left|\sum_{|x|^2=\lambda_l}f(y-x)\right|\] for
functions $f:\mathbb{Z}^n\to\mathbb{C}^n$ are bounded on $\ell^p$ for all $p>1$
when the ambient dimension $n$ is at least five.
