  In many data structure settings, it has been shown that using "double
hashing" in place of standard hashing, by which we mean choosing multiple hash
values according to an arithmetic progression instead of choosing each hash
value independently, has asymptotically negligible difference in performance.
We attempt to extend these ideas beyond data structure settings by considering
how threshold arguments based on second moment methods can be generalized to
"arithmetic progression" versions of problems. With this motivation, we define
a novel "quasi-random" hypergraph model, random arithmetic progression (AP)
hypergraphs, which is based on edges that form arithmetic progressions and
unifies many previous problems. Our main result is to show that second moment
arguments for 3-NAE-SAT and 2-coloring of 3-regular hypergraphs extend to the
double hashing setting. We leave several open problems related to these
quasi-random hypergraphs and the thresholds of associated problem variations.
