This is often the case, when the OP is not willed to enlighten the background of his problem a bit, in order to avoid a breach of secrecy and to save the mankind from total demolishment.

I elaborated on what the sequence of numbers is used for (picking subsets from a set), what properties it should have, and a simple way to test it. The only thing I didn't post was the actual code of the implementation I came up with.

Summarized ...

... I need to generate a sequence of 65536 (generalized: 2^m) numbers which
a) contains each number from 0 to 65535 (generalized: (2^m)-1) exactly once
and
b) the number of '0' bits in element n+1 must be greater or equal than the number of '0' bits in element n.