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53
53 is an integer.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 53
- 3 Partitions of 53
- 4 Roots and powers of 53
- 5 Logarithms and 53rd powers
- 6 Values for number theoretic functions with 53 as an argument
- 7 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −53, 53
- 8 Factorization of 53 in some quadratic integer rings
- 9 Representation of 53 in various bases
- 10 See also
Membership in core sequences
Odd numbers | ..., 47, 49, 51, 53, 55, 57, 59, ... | A005408 |
Prime numbers | ..., 41, 43, 47, 53, 59, 61, ... | A000040 |
Squarefree numbers | ..., 46, 47, 51, 53, 55, 57, 58, ... | A005117 |
In Pascal's triangle, 53 occurs twice. (In Lozanić's triangle, 53 occurs four times).
Sequences pertaining to 53
Multiples of 53 | 0, 53, 106, 159, 212, 265, 318, 371, 424, 477, 530, 583, 636, ... | |
sequence beginning at 15 | 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ... | A033480 |
Partitions of 53
There are 329931 partitions of 53. Of these, the ones consisting of distinct which the of the [FINISH WRITING]
Roots and powers of 53
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Logarithms and 53rd powers
In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.
As above, irrational numbers in the following table are truncated to eight decimal places.
TABLE GOES HERE
See A089081 for the 26th powers of integers.
Values for number theoretic functions with 53 as an argument
TABLE GOES HERE
Factorization of some small integers in a quadratic integer ring adjoining the square roots of −53, 53
The commutative quadratic integer ring with unity , with units of the form (), is a unique factorization domain.
TABLE GOES HERE
is not a unique factorization domain either. But the range of 1 through 20 does not provide as interesting a window for the of the [FINISH WRITING]
Factorization of 53 in some quadratic integer rings
As was mentioned above, 26 is the product of two primes in . But it has different factorizations in some quadratic integer rings.
TABLE
REMARKS
Representation of 53 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 110101 | 1222 | 311 | 203 | 125 | 104 | 65 | 58 | 53 | 49 | 45 | 41 | 3B | 38 | 35 | 32 | 2H | 2F | 2D |
Note that the hexadecimal digits of 53 are the same as its decimal digits, just reversed.
Far more interesting than that, however, is the fact that 53 is not palindromic in any of the bases shown here. In fact, it's not palindromic in any base from binary to base 51. This means that 53 is a strictly non-palindromic number (see A016038).
See also
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 |