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# 100

Please do not rely on any information it contains.

100 is the square of 10, and the smallest square that is the sum of four consecutive cubes: 1 3 + 2 3 + 3 3 + 4 3 = 100.

## Membership in core sequences

 Even numbers ..., 94, 96, 98, 100, 102, 104, 106, ... A005843 Composite numbers ..., 96, 98, 99, 100, 102, 104, 105, ... A002808 Perfect squares ..., 49, 64, 81, 100, 121, 144, 169, ... A000290 Abundant numbers ..., 88, 90, 96, 100, 102, 104, 108, ... A005101 Loeschian numbers ..., 91, 93, 97, 100, 103, 108, 109, ... A003136

In Pascal's triangle, 100 occurs only twice, namely in row 64, in the second and next to last positions. But it also appears in a subtler way, as the sum of the numbers in row 6: 1 + 6 15 + 20 + 15 + 6 + 1 = 64.

## Sequences pertaining to 64

 Multiples of 100 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, ... ${\displaystyle 3x-1}$ sequence beginning at 100 100, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122, 61, 182, 91, 272, 136, ... A008903 ${\displaystyle 3x+1}$ sequence beginning at 33 33, 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, ... A008880

## Partitions of 100

There are X partitions of 100. [FINISH WRITING]

## Roots and powers of 100

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

TABLE GOES HERE

## Logarithms and 100th powers

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

REMARKS

TABLE GOES HERE

TABLE GOES HERE

## References

 ${\displaystyle -1}$ 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