Imagine you have an integer x, and you want to find the closest integer (unequal to x) that has the same hamming weight.

There is a relevant Q&A on SO, link at the bottom.

Here's an alternative with fewer operations than anything mentioned there: let y = -x & (x + 1) in x ^ y ^ (y >> 1)

How does that work? I don't really know, I pulled this out of the void with a SAT solver. Basically magic.

SO: (careful, the decent answers are buried deep) https://stackoverflow.com/q/38523733/555045