OEIS/Harrows

In the early 1930s Erdős introduced a covering system (also called complete residue systems) as a collection

$\{a_{1}(\mathrm {mod} \ {n_{1}}),\ \ldots ,\ a_{k}(\mathrm {mod} \ {n_{k}})\}$

of finitely many residue classes $a_{i}(\mathrm {mod} \ {n_{i}})=\{a_{i}+n_{i}x:\ x\in \mathbb {Z} \}$

In the following we will use a slightly different definition:

1. negative integers are excluded,
2. there may be infinitely many residue classes, and
3. any non-negative integer is covered by exactly one residue class only.

We will call such a modified covering system a harrow.