digitaddition generator

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 and $2|b$, the $n|̸2$ will lack digitaddition generators.