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# 52

Please do not rely on any information it contains.

52 is an integer.

## Membership in core sequences

 Even numbers ..., 46, 48, 50, 52, 54, 56, 58, ... A005843 Composite numbers ..., 49, 50, 51, 52, 54, 55, 56, ... A002808 Deficient numbers ..., 49, 50, 51, 52, 53, 55, 57, ... A005100 Bell numbers 1, 1, 2, 5, 15, 52, 203, 877, ... A000110 Sums of 2 squares ..., 45, 49, 50, 52, 53, 58, 61, ... A001481 Loeschian numbers ..., 43, 48, 49, 52, 57, 61, 63, ... A003136 Binary tree numbers 2, 7, 52, 2133, 2590407, ... A005588

## Sequences pertaining to 52

 Multiples of 52 0, 52, 104, 156, 208, 260, 312, 364, 416, 468, 520, 572, 624, ... ${\displaystyle 3x+1}$ sequence beginning at 9 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, ... A033479

## Partitions of 52

There are 281589 partitions of 52.

The Goldbach representations of 52 are 47 + 5 = 41 + 11 = 23 + 29.

## Roots and powers of 52

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

PLACEHOLDER

PLACEHOLDER

## Factorization of some small integers in a quadratic integer ring adjoining the square roots of −52, 52

Since 52 is not squarefree, [FINISH WRITING]

PLACEHOLDER

## Representation of 52 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 110100 1221 310 202 124 103 64 57 52 48 44 40 3A 37 34 31 2G 2E 2C

 ${\displaystyle -1}$ 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