Erdős–Oler-type conjecture for triangular numbers

Let $n>3$ be a triangular number, and consider the smallest triangle containing $n$ disks and the smallest triangle containing $n-1$ disks. Erdős–Oler-type conjecture. The smallest triangle containing $n$ disks is the same as that containing $n-1$ disks. This is presented as a new version of the long-standing Erdős–Oler conjecture. The claim is not established in the source and remains open.