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# 121

Please do not rely on any information it contains.

121 is an integer. It is the only known square of the form $1+p+p^{2}+p^{3}+p^{4}$ , where $p$ is prime (in this case, $p=3$ ).

## Membership in core sequences

 Odd numbers ..., 114, 116, 118, 121, 122, 124, 126, ... A005408 Composite numbers ..., 118, 119, 120, 121, 122, 123, 124, ... A002808 Perfect squares ..., 64, 81, 100, 121, 144, 169, 196, ... A000290 Central polygonal numbers ..., 79, 92, 106, 121, 137, 154, 172, ... A000124 Numbers that are the sum of 2 squares ..., 113, 116, 117, 121, 122, 125, 128, ... A001481 Loeschian numbers ..., 111, 112, 117, 121, 124, 127, 129, ... A003136

## Sequences pertaining to 121

 Multiples of 121 121, 242, 363, 484, 605, 726, 847, 968 ... $3x+1$ sequence starting at 27 ..., 161, 484, 242, 121, 364, 182, 91, 274, ... A008884

## Partitions of 121

There are 2056148051 partitions of 121. Of these, there is the of the [FINISH WRITING]

## Roots and powers of 121

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

TABLE GOES HERE

## Logarithms and 121st 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 121 in some quadratic integer rings

As was mentioned above, 121 is the square of 11. But it has different factorizations in some quadratic integer rings.

TABLE GOES HERE

## Representation of 121 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 1111001 11111 1321 441 321 232 171 144 121 100 A1 94 89 81 79 72 6D 67 61

 $-1$ 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