In the spirit of Lehmer's speculation that Ramanujan's tau-function never vanishes, it is natural to ask whether any given integer $\alpha$ a value $\tau(n)$. For odd $\alpha$, Murty, and Shorey proved $\tau(n)\neq \alpha$ for sufficiently large $n$. Several recent papers have identified explicit examples which are not tau-values. Here we apply these results (most notably work Bennett, Gherga, ...

presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. the method is easy to u...