senary

A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like the decimal base 10, the base is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to the senary system.

==Formal definition== The standard set of digits in the senary system is \mathcal{D}_6 = \lbrace 0, 1, 2, 3, 4, 5\rbrace, with the linear order 0 . Let \mathcal{D}_6^* be the Kleene closure of \mathcal{D}_6, where ab is the operation of string concatenation for a, b \in \mathcal{D}^*. The senary number system for natural numbers \mathcal{N}_6 is the quotient set \mathcal{D}_6^* / \sim equipped with a shortlex order, where the equivalence class \sim is \lbrace n \in \mathcal{D}_6^*, n \sim 0n \rbrace. As \mathcal{N}_6 has a shortlex order, it is isomorphic to the natural numbers \mathbb{N}.