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.

Title	parasitic number
Canonical name	ParasiticNumber
Date of creation	2013-03-22 16:22:17
Last modified on	2013-03-22 16:22:17
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	4
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A63
Synonym	left-transposable integer