181 (one hundred
ndeighty-one) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
180
__NOTOC__
Year 180 ( CLXXX) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Rusticus and Condianus (or, less frequently, year 933 '' Ab ...
and preceding
182.
In mathematics
* 181 is an
odd number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because
\begin
-2 \cdot 2 &= -4 \\
0 \cdot 2 &= 0 \\
41 ...
* 181 is a
centered number
The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers of dots with a constant number of sides. Each side of a polygonal layer contains one more dot than each side i ...
** 181 is a
centered pentagonal number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the ...
** 181 is a
centered 12-gonal number
** 181 is a
centered 18-gonal number
** 181 is a
centered 30-gonal number
** 181 is a
centered square number
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each cen ...
** 181 is a
star number
A star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on.
The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n'' − 1) + 1. The ...
that represents a centered
hexagram
, can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green).
A hexagram ( Greek language, Greek) or sexagram (Latin) is a six-pointed ...
(as in the game of
Chinese checkers)
* 181 is a
deficient number
In number theory, a deficient number or defective number is a number ''n'' for which the sum of divisors of ''n'' is less than 2''n''. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than ''n''. For ex ...
, as 1 is less than 181
* 181 is an
odious number
In number theory, an odious number is a positive integer that has an odd number of 1s in its binary expansion.
In computer science, an odious number is said to have odd parity.
Examples
The first odious numbers are:
Properties
If a(n) denotes ...
* 181 is a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
** 181 is a
Chen prime
A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem.
The Chen primes are named after Chen Jingru ...
** 181 is a
dihedral prime
A dihedral prime or dihedral calculator prime is a prime number that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation (normally or upside down), and surface (actual display or reflectio ...
** 181 is a
full reptend prime
In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat q ...
** 181 is a
palindromic prime
In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such ...
** 181 is a
strobogrammatic prime, the same when viewed upside down
** 181 is a
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...
with
179
* 181 is a
square-free number
In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, is square-fr ...
* 181 is an
undulating number An undulating number is a number that has the digit form ABABAB... when in the base 10 number system. It is sometimes restricted to non-trivial undulating numbers which are required to have at least three digits and A ≠ B. The first few such numbe ...
, if written in the
ternary
Ternary (from Latin ''ternarius'') or trinary is an adjective meaning "composed of three items". It can refer to:
Mathematics and logic
* Ternary numeral system, a base-3 counting system
** Balanced ternary, a positional numeral system, useful ...
, the
negaternary, or the
nonary
A ternary numeral system (also called base 3 or trinary) has 3 (number), three as its radix, base. Analogous to a bit, a ternary numerical digit, digit is a trit (trinary digit). One trit is equivalent to binary logarithm, log2 3 (about 1.5 ...
numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using Numerical digit, digits or other symbols in a consistent manner.
The same s ...
s
* 181 is the difference of
2 square number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals ...
s: 91
2 – 90
2
* 181 is the sum of
2