05 What is the Mersenne Sequence?

A000225 – OEIS

The Mersenne sequence contains numbers of the form

When represented in the dual system, Mersenne numbers show up as columns of ones, that is, numbers consisting exclusively of ones.

The first numbers are
0,
1,
3,
7,
15,
31,
63,
127,
255,
511,
1023,
2047,
4095,
8191,
16383,
32767,
65535,
131071,
262143,
524287,
1048575,
2097151,
4194303,
8388607,
16777215,
33554431,
67108863,
134217727,
268435455,
536870911,
1073741823,
2147483647,
4294967295