yeah, calendar manipulation is trickier than it looks. If you use day-of-week, you have an odd number of days. If you use day of month, many months have an odd number. If you use day of year (%j), most years have an odd number.

There's many such examples - every 1, 2, 3, 4, 6 hours works - but every 5 hours doesn't. But every 2 days and every 14 days are requirements I've met IRL.