In mathematics, 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:

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.

An n-parasitic number can be derived by starting with a digit k (which should be equal to n or greater) in the rightmost (units) place, and working up one digit at a time. For example, for n = 4 and k = 7

So 179487 is a 4-parasitic number with units digit 7. Others are 179487179487, 179487179487179487, etc.

Notice that the repeating decimal

Thus

In general, an n-parasitic number can be found as follows. Pick a one digit integer k such that k ≥ n, and take the period of the repeating decimal k/(10n−1). This will be ${\displaystyle {\frac {k}{10n-1}}(10^{m}-1)}$ where m is the length of the period; i.e. the multiplicative order of 10 modulo (10n − 1).