Leap years starting on Friday share this characteristic.
In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Friday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks).
Forty-three common years per cycle or exactly 10.75% start on a Saturday.
In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks).
Each of the seven two-letter sequences occurs once within a cycle, and every common letter thrice.