Just forget 4000MHz.
That would require very good CPU individual to get InfinityFabric running in sync with memory.
3800Mhz is more realistic, though still needs good CPU and might not work without some manual tweaking.
And there's no sense in paying luxury from 16GB:
Memory capacity you don't have has no speed, or at most negative speed.
So unless you're just after overclocking/benchmarking record making, you should put extra money toward capacity to last for years.
Besides if you get Samsung B-die DIMMs 16GB ones are dual rank, which boosts gaming performance per clock.