  Weird numbers are abundant numbers that are not pseudoperfect. Since their
introduction, the existence of odd weird numbers has been an open problem. In
this work, we describe our computational effort to search for odd weird
numbers, which shows their non-existence up to $10^{21}$. We also searched up
to $10^{28}$ for numbers with an abundance below $10^{14}$, to no avail. Our
approach to speed up the search can be viewed as an application of reverse
search in the domain of combinatorial optimization, and may be useful for other
similar quest for natural numbers with special properties that depend crucially
on their factorization.
