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 $0 < n < b$ and $2|b$ , the $n \not\vert 2$ will lack digitaddition generators.