Parasitic number

An n-parasitic number (in base 10) is a positive natural number which, when multiplied by n, results in movement of the last digit of its decimal representation to its front. Here n is itself a single-digit positive natural number. In other words, the decimal representation undergoes a right circular shift by one place. For example:

4 × 128205 = 512820, so 128205 is 4-parasitic.

Most mathematicians do not allow leading zeros to be used, and that is a commonly followed convention.

So even though 4 × 25641 = 102564, the number 25641 is not 4-parasitic.