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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
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, ...
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.

7.41619848 A010508 55 2 3025
3.80295246 A010626 55 3 166375
2.72326981 A011048 55 4 9150625
2.22880738 A011140 55 5 27680640625
1.95011601 55 6 1522435234375
1.77265100 55 7 83733937890625
1.65023326 55 8 4605366583984375
1.56089479 55 9 253295162119140625
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 , with units of the form (), is not a unique factorization domain. Neither is .

2 Irreducible
3
4 2 2
5 Irreducible
6 2 × 3 2 × 3 OR
7 Irreducible
8 2 3
9 3 2 3 2 OR
10 2 × 5
11 Irreducible
12 2 2 × 3
13 Irreducible Irreducible despite positive Legendre symbol
14 2 × 7 OR 2 × 7
15 3 × 5
16 2 4 OR 2 4
17 Irreducible Irreducible despite positive Legendre symbol
18 2 × 3 2
19 Irreducible
20 2 2 × 5 OR

Factorization of 55 in some quadratic integer rings

As was mentioned above, 55 is a squarefree semiprime in . 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
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