Nonary is a base- numeral system

Numeral system

A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....

, typically using the digit

Numerical digit

A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...

s 0-8, but not the digit 9.

The first few numbers in nonary and decimal are:

Nonary	1	2	3	4	5	6	7	8	10	11	12	13	14
Decimal	1	2	3	4	5	6	7	8	9	10	11	12	13

The multiplication table in nonary is:

*	1	2	3	4	5	6	7	8
1	1	2	3	4	5	6	7	8
2	2	4	6	8	11	13	15	17
3	3	6	10	13	16	20	23	26
4	4	8	13	17	22	26	31	35
5	5	11	16	22	27	33	38	44
6	6	13	20	26	33	40	46	53
7	7	15	23	31	38	46	54	62
8	8	17	26	35	44	53	62	71

Nonary notation can be used as a concise representation of ternary

Ternary numeral system

Ternary is the base- numeral system. Analogous to a bit, a ternary digit is a trit . One trit contains \log_2 3 bits of information...

 data. This is similar to using quaternary

Quaternary numeral system

Quaternary is the base- numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation and the characteristics of the representations of...

 notation for binary

Binary numeral system

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

 data, though the digit set is closer in size to octal

Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

.

Except for three, no primes in nonary end in 0, 3 or 6, since any nonary number ending in 0, 3 or 6 is divisible by three.

A nonary number is divisible by two, four or eight, if the sum of its digits is also divisible by two, four or eight respectively.

If x is a triangular number, so is 9x+1. This means that one finds 3, 31, 311, 3111, 31111... in the triangular number

Triangular number

A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

s. Likewise, 6, 61, 611, 6111, ....

In popular culture

Although the term "Nonary" is used in describing the written form of the language used by the fictional civilization, The Culture

The Culture

The Culture is a fictional interstellar anarchist, socialist, and utopian society created by the Scottish writer Iain M. Banks which features in a number of science fiction novels and works of short fiction by him, collectively called the Culture series....

, found in Iain M. Banks' books, the description on page 119 of Excession

Excession

Excession, first published in 1996, is Scottish writer Iain M. Banks's fourth science fiction novel to feature the Culture. It concerns the response of the Culture and other interstellar societies to an unprecedented alien artifact, the Excession of the title.The book is largely about the response...

reads more like it's based on a binary system with a 9-bit 'byte'.