They are called Weaver Pivot Rings/Bases and they were discontinued sometime in the 1980's I believe. They fell out of favor with the public when gunwriters back in the day claimed they would never hold zero swinging back and forth like that. Obviously, this was decided over a typewriter and certainly not at the range.
They are a specialized base that only accepts a set of Weaver Pivot rings. A Pivot base part number code uses the regular base number preceded by a 1. For example the regular base for a Remington 760 is #62, the pivot base is #162.
I have them on several of my 760's and on both my Marlin 336's. You can find the bases and rings on Fleabay used often enough.
I also, in addition to the sets I have on my rifles, have about 5 bases for Remington 742/760's, 2 bases for Remington 7400/7600's, 1 base for a Marlin 336 and 5 or 6 sets of pivot rings to go on the bases.
Yeah, you could say I'm a fan.
Old school El Paso Weaver V4.5 on a Marlin 336 in .35 Remington, closed & swung over: