Calendar recurrence

There are 14 possible Gregorian calendars, given that a Gregorian year can begin on any day of the week and has either 365 or 366 days. In this post I'm going to explore how often each of those calendars can be reused.

Leap years cycle through beginning on each day of the week, starting two days earlier in the week than the previous leap year. Thus, a 366-day calendar can only be reused once every 28 years:

365-day calendars recur more frequently, though, because of the insertion of leap years, not quite so regularly. This year's calendar started on Saturday, as did 2011's calendar, and before that 2005's. In general, non-leap year calendars recur after either 6 or 11 years: after 6 years for years immediately following a leap year, after 11 years for other non-leap years. That means a non-leap calendar recurs after 6 years, then after 11 years, then after another 11 years, then after 6 years again, repeating in what, like leap recurrence, is a 28-year cycle.