Roundtrip flight from USA to beijing. Separate roundtrip flight from beijing to hong kong.

I have a flight from Texas to beijing and i land in beijing at 1630 on 3/13/2018. I really wanted to fly into hong kong but it was cheaper to fly into beijing. I want to hang out in beijing for 2 days and then book a separate flight from beijing to hong kong for 4 days from 3/15-3-19 at 1200 i will be back at beijing airport. Then i will fly back to Texas on 3-19 at 1530. Will I need any special visa?