If you go with the encounters per adventuring day guidelines and cross reference the experience per encounter with the experience required to level up, it’s almost exactly one level every other adventuring day. Obviously it will take more sessions than that if you have fewer encounters per adventuring day than the guidelines suggest and/or fewer than one adventuring day per session, which is why I said it depends entirely on how many encounters the group is having per session and how hard those encounters are.
That said, a level up every other session does at least seem to have been consistent with the designers’ intent at the time they were originally designing those guidelines. Mike Mearls said on a Happy Fun Hour that this was their intention, and that he highly recommends groups try leveling up at that pace. I’d cite it if Happy Fun Hour weren’t defunct.