So Consecutive Sudoku really annoys me because it always ends up solving as non-consecutive Sudoku - and any really cool combinatorial tricks end up being drowned out by the non-consecutive logic.
I believe it was Bastien who first introduced the idea of a Consecutive pair to the Daily League, and it's a really good idea. I was quite tempted to stick with the ubiquitous bar notation for this puzzle in an attempt to reclaim it, but I will stick with what Bastien used for now. Marked pairs of adjacent cells must contain consecutive numbers; there is no restriction on adjacent cells with no marking. Enjoy!