exupero's blog

Recurrence intervals near non-leap year centennials

In the previous post I described how often year and month calendars can be reused, and while the sequences of intervals I outlined occur most of the time, there are exceptions, namely around years divisible by four that aren't leap years, such as 1900 and 2100 (but not 2000).

While annual, non-leap year calendars usually recur after 6 years, 11 years, and 11 years (6-11-11), when intervals get close to centennial non-leap years they can recur in several other sequences: 6-6-11, 6-12-11-11, 6-6-6-11-11, 6-11-11-12, or 6-11-12-11.

Leap year recurrence is also affected. Instead of the usual 28-year recurrence, a leap year crossing a centennial non-leap year can recur in 12 years or in 40 years.

For month recurrence, the usual interval sequence of 6-11-6-5 breaks down and becomes 6-11-6-6-6-5, 6-12-11-6-5, 6-11-12-6-5, 6-6-6-11-6-5, or 7-5-6-11-6-5. The most common pattern seems to be 6-11-6-6-6-5.