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Homedigitaddition generator

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

Synonym:

digit addition generator, digit-addition generator

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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