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33
33 is an integer, the largest that is not a sum of distinct triangular numbers.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 33
- 3 Partitions of 33
- 4 Roots and powers of 33
- 5 Logarithms and 33rd powers
- 6 Values for number theoretic functions with 33 as an argument
- 7 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −33, 33
- 8 Factorization of 33 in some quadratic integer rings
- 9 Representation of 33 in various bases
- 10 See also
Membership in core sequences
Odd numbers | ..., 27, 29, 31, 33, 35, 37, 39, ... | A005408 |
Semiprimes | ..., 22, 25, 26, 33, 34, 35, 38, ... | A001358 |
Squarefree numbers | ..., 29, 30, 31, 33, 34, 35, 37, ... | A005117 |
Composite numbers | ..., 28, 30, 32, 33, 34, 35, 36, ... | A002808 |
Deficient numbers | ..., 29, 31, 32, 33, 34, 35, 37, ... | A005100 |
Lucky numbers | ..., 21, 25, 31, 33, 37, 43, 49, ... | A000959 |
Sequences pertaining to 33
Multiples of 33 | 0, 33, 66, 99, 132, 165, 198, 231, 264, 297, 330, 363, 396, ... | |
sequence starting at 33 | 33, 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, ... | A008880 |
Partitions of 33
There are 10143 partitions of 33.
Although there are no partitions of 33 into distinct triangular numbers, there are plenty of triangular number partitions with repeated numbers, such as: 28 + 3 + 1 + 1, 21 + 10 + 1 + 1, 15 + 15 + 3, etc.
Roots and powers of 33
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Logarithms and 33rd powers
In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.
If is not a multiple of 67, then either or is. Hence the formula for the Legendre symbol .
As above, irrational numbers in the following table are truncated to eight decimal places.
TABLE GOES HERE
Values for number theoretic functions with 33 as an argument
TABLE GOES HERE
Factorization of some small integers in a quadratic integer ring adjoining the square roots of −33, 33
TABLE GOES HERE
Factorization of 33 in some quadratic integer rings
PLACEHOLDER
TABLE GOES HERE
Representation of 33 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 100001 | 1020 | 201 | 113 | 53 | 45 | 41 | 36 | 33 | 30 | 29 | 27 | 25 | 23 | 21 | 1G | 1F | 1C | 1D |
33 is palindromic in binary, decimal and base 32, and trivially palindromic in base 34 and higher.
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 |