This number sequence is similar to the Mersenne sequence, except that it contains the Fermat number sequence. The calculation of the numbers is done with the formula

The first numbers are

2,

3,

5,

9,

17,

33,

65,

129,

257,

513,

1025,

2049,

4097,

8193,

16385,

32769,

65537,

131073,

262145,

524289,

1048577,

2097153,

4194305,

8388609,

16777217,

33554433,

67108865,

134217729,

268435457,

536870913,

1073741825,

2147483649