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# 128

Please do not rely on any information it contains.

128 is the seventh power of 2.

## Membership in core sequences

 Even numbers ..., 122, 124, 126, 128, 130, 132, 134, ... A005843 Composite numbers ..., 124, 125, 126, 128, 129, 130, 132, ... A002808 Powers of 2 ..., 16, 32, 64, 128, 256, 512, 1024, ... A000079 Numbers that are the sum of two squares ..., 121, 122, 125, 128, 130, 136, 137, ... A001481

## Sequences pertaining to 128

 Multiples of 128 0, 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280, 1408, 1536, ... $3x+1$ sequence beginning at 75 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1, ... A258056 $3x-1$ sequence beginning at 87 ..., 920, 460, 230, 115, 344, 172, 86, 43, 128, 64, 32, 16, 8, 4, 2, 1, ... A008899

## Partitions of 128

There are 4351078600 partitions of 128.

The Goldbach representations of 128 are: 109 + 19 = 97 + 31 = 67 + 61 = 128.

## Roots and powers of 128

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

TABLE GOES HERE

## Logarithms and 128th powers

In the OEIS specifically and mathematics in general, $\log x$ refers to the natural logarithm of $x$ , 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

TABLE GOES HERE

## Factorization of 8 in some quadratic integer rings

In $\mathbb {Z}$ , 128 has the prime factorization of 2 7. But it has different factorizations in some quadratic integer rings.

TABLE GOES HERE

## Representation of 128 in various bases

TABLE GOES HERE

 $-1$ 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