let $a$ be the first weyl algebra, in the euler gradation. we classify graded rings $b$ such that $gr-a$ and $gr-b$ are equivalent (we say that $a$ and $b$ are graded equivalent), and produce some surprising examples. in particular, we show that $a$ is graded equivalent to an idealizer in a localization of $a$. in the process, we derive a concise new characterization of equivalences of graded module categories that generalizes the classical morita theorems.