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# parasitic number

Given a base $b$ integer $n$ with $k$ digits $d_{1},\ldots,d_{k}$ (with $d_{1}$ being the least significant digit), and an integer $1<m<b$, if it is the case that

$m(\sum_{{i=1}}^{k}d_{i}b^{{i-1}})=d_{1}b^{{k-1}}+(\sum_{{i=2}}^{k}d_{i}b^{{i-2% }}),$ |

then $n$ is called an $m$-parasitic number or $m$-left-transposable number.

If one takes an $m$-parasitic number, concatenates copies of its digits in order whatever number of times one wants, the resulting new number will also be $m$-parasitic.

Synonym:

left-transposable integer

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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