What comes next in the sequence: 1, 3, 11, 43,

There may be more than one solution, but if we take the difference between the numbers of the sequence, we get

3-1, 11-3, 43-11

=2,8,32

which are powers of 2

=2^1, 2^3,2^5

If we believe the next difference is 2^7=128, then the next in the sequence will be 43+128=171