55

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55 is an integer.

Membership in core sequences

Odd numbers	..., 49, 51, 53, 55, 57, 59, 61, ...	A005843
Squarefree numbers	..., 59, 61, 62, 55, 66, 67, 69, ...	A005117
Semiprimes	..., 46, 49, 51, 55, 57, 58, 62, ...	A001358
Composite numbers	..., 51, 52, 54, 55, 56, 57, 58, ...	A002808
Fibonacci numbers	..., 13, 21, 34, 55, 89, 144, 233, ...	A000045
Triangular numbers	..., 28, 36, 45, 55, 66, 78, 91, ...	A000217
Square pyramidal numbers	..., 5, 14, 30, 55, 91, 140, 204, ...	A000330
${\frac {\binom {3n}{n}}{2n+1}}$	1, 1, 3, 12, 55, 273, 1428, ...	A001764

Notice that 55 is the largest triangular number in the Fibonacci sequence, and in both sequences occurs at position 10. In Pascal's triangle, 55 occurs four times, two of those times being in the triangular numbers columns.

Sequences pertaining to 55

Multiples of 55	0, 55, 110, 165, 220, 275, 330, 385, 440, 495, 550, ...
$3x+1$ sequence starting at 97	97, 292, 146, 73, 220, 110, 55, 166, 83, 250, 125, ...	A008873

Partitions of 55

There are 451276 partitions of 55. Of these, only the of the [FINISH WRITING]

Roots and powers of 55

In the table below, irrational numbers are given truncated to eight decimal places.

${\sqrt {55}}$	7.41619848	A010508	55 2	3025
${\sqrt[{3}]{55}}$	3.80295246	A010626	55 3	166375
${\sqrt[{4}]{55}}$	2.72326981	A011048	55 4	9150625
${\sqrt[{5}]{55}}$	2.22880738	A011140	55 5	27680640625
${\sqrt[{6}]{55}}$	1.95011601		55 6	1522435234375
${\sqrt[{7}]{55}}$	1.77265100		55 7	83733937890625
${\sqrt[{8}]{55}}$	1.65023326		55 8	4605366583984375
${\sqrt[{9}]{55}}$	1.56089479		55 9	253295162119140625
${\sqrt[{10}]{55}}$	1.49291908		55 10	13931233916552734375

Logarithms and 55th powers

PLACEHOLDER

Values for number theoretic functions with 55 as an argument

PLACEHOLDER

Factorization of some small integers in a quadratic integer ring adjoining the square roots of 55 and −55

The commutative quadratic integer ring with unity $\mathbb {Z} [{\sqrt {55}}]$, with units of the form $\pm (89+12{\sqrt {55}})^{n}\,$ ($n\in \mathbb {Z}$), is not a unique factorization domain. Neither is ${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-55}})}$.

$n$	${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-55}})}$	$\mathbb {Z} [{\sqrt {55}}]$
2	Irreducible
3
4	2 2
5	Irreducible	$(15-2{\sqrt {55}})(15+2{\sqrt {55}})$
6	2 × 3	2 × 3 OR $(-1)(7-{\sqrt {55}})(7+{\sqrt {55}})$
7	Irreducible
8	2 3
9	3 2	3 2 OR $(8-{\sqrt {55}})(8+{\sqrt {55}})$
10	2 × 5	$2(15\pm 2{\sqrt {55}})$
11	Irreducible	$(-1)(22-3{\sqrt {55}})(22+3{\sqrt {55}})$
12	2 2 × 3
13	Irreducible	Irreducible despite positive Legendre symbol
14	2 × 7 OR $\left({\frac {1}{2}}-{\frac {\sqrt {-55}}{2}}\right)\left({\frac {1}{2}}+{\frac {\sqrt {-55}}{2}}\right)$	2 × 7
15	3 × 5	$3(15\pm 2{\sqrt {55}})$
16	2 4 OR $\left({\frac {3}{2}}-{\frac {\sqrt {-55}}{2}}\right)\left({\frac {3}{2}}+{\frac {\sqrt {-55}}{2}}\right)$	2 4
17	Irreducible	Irreducible despite positive Legendre symbol
18	2 × 3 2
19	Irreducible	$(-1)(6-{\sqrt {55}})(6+{\sqrt {55}})$
20	2 2 × 5 OR $\left({\frac {5}{2}}-{\frac {\sqrt {-55}}{2}}\right)\left({\frac {5}{2}}+{\frac {\sqrt {-55}}{2}}\right)$	$2^{2}(15\pm 2{\sqrt {55}})$

Factorization of 55 in some quadratic integer rings

As was mentioned above, 55 is a squarefree semiprime in $\mathbb {Z}$. But it has different factorizations in some quadratic integer rings.

PLACEHOLDER FOR TABLE

Representation of 55 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	110111	2001	313	210	131	106	67	61	59	50	47	43	3D	3A	37	34	31	2H	2F

See also

Some integers

							$-1$
0	1	2	3	4	5	6	7	8	9
10	11	12	13	14	15	16	17	18	19
20	21	22	23	24	25	26	27	28	29
30	31	32	33	34	35	36	37	38	39
40	41	42	43	44	45	46	47	48	49
					1729