Given an integer $m$ consisting of $k$ digits $d_{x}$ in base $b$, it follows that
 $m+\sum_{i=0}^{k-1}d_{i+1}b^{i}=n$
, another integer. Then $m$ is said to be the digitaddition generator of $n$.
In a randomly chosen range of $2b$ consecutive integers, most will have a digitaddition generator and one or two might have none (such integers are called self numbers). If the range falls near a multiple of $b^{2}$, it might contain a few numbers with two digitaddition generators. If the range includes $0 and $2|b$, the $n\not|2$ will lack digitaddition generators.