183 (number)

← 182 183 184 →
← 180 181 182 183 184 185 186 187 188 189 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred eighty-three
Ordinal	183rd (one hundred eighty-third)
Factorization	3 × 61
Divisors	1, 3, 61, 183
Greek numeral	ΡΠΓ´
Roman numeral	CLXXXIII
Binary	101101112
Ternary	202103
Senary	5036
Octal	2678
Duodecimal	13312
Hexadecimal	B716

183 (one hundred [and] eighty-three) is the natural number following 182 and preceding 184.

In mathematics

183 is a perfect totient number, a number that is equal to the sum of its iterated totients. ^[1]

Because ${\displaystyle 183=13^{2}+13+1}$, it is the number of points in a projective plane over the finite field ${\displaystyle \mathbb {Z} _{13}}$. ^[2] 183 is the fourth element of a divisibility sequence ${\displaystyle 1,3,13,183,\dots }$ in which the ${\displaystyle n}$th number ${\displaystyle a_{n}}$ can be computed as

$${\displaystyle a_{n}=a_{n-1}^{2}+a_{n-1}+1={\bigl \lfloor }x^{2^{n}}{\bigr \rfloor },}$$

for a transcendental number ${\displaystyle x\approx 1.38509}$. ^{[3] [4]} This sequence counts the number of trees of height ${\displaystyle \leq n}$ in which each node can have at most two children. ^{[3] [5]}

There are 183 different semiorders on four labeled elements. ^[6]

See also

• The year AD 183 or 183 BC
• List of highways numbered 183
• All pages with titles containing 183

References

1. Sloane, N. J. A. (ed.). "SequenceA082897(Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA002061(Central polygonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA002065". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Dubickas, Artūras (2022). "Transcendency of some constants related to integer sequences of polynomial iterations". Ramanujan Journal. 57 (2): 569–581. doi:10.1007/s11139-021-00428-5. MR   4372232. S2CID   236289092.
5. Kalman, Stan C.; Kwasny, Barry L. (January 1995). "Tail-recursive distributed representations and simple recurrent networks". Connection Science. 7 (1): 61–80. doi:10.1080/09540099508915657.
6. Sloane, N. J. A. (ed.). "SequenceA006531(Semiorders on n elements)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.