non-standard positional numeral system

Non-standard positional numeral systems here designates numeral systems that may loosely be described as positional systems, but that do not entirely comply with the following description of standard positional systems:

In a standard positional numeral system, the base b is a positive integer, and b different numerals are used to represent all non-negative integers. Each numeral represents one of the values 0, 1, 2, etc., up to b-1, but the value also depends on the position of the digit in a number. The value of a digit string like in base b is given by the polynomial form

.