In this
Polyominous puzzle, a pair of horizontally or vertically adjacent cells with a white circle between them must contain two consecutive numbers, and a pair of horizontally or vertically adjacent cells with a black circle between them must contain one number which is two times the other number. If two adjacent cells do not have a circle between them, then neither of these conditions may be true. The rules are otherwise unchanged.

The inspiration for this one comes from a puzzle called Kropki (which is apparently the Polish word for "dot"), but I'd be remiss not to mention
cyrebjr's puzzles, as well.