A common year starting on Saturday is any non-leap year (i.e. a year with 365 days) that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2011 and the next one will be 2022 in the Gregorian calendar or, likewise, 2006 and 2017 in the obsolete Julian calendar, see below for more.
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If the preceding year is a common year starting on Friday, then the year begins in ISO week 52; if the preceding year is a leap year starting on Thursday, then the year begins in ISO week 53.
Gregorian Calendar
In the (currently used) Gregorian calendar, the 15 types of years repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Saturday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.
Julian Calendar
In the now-obsolete Julian calendar, the 15 types of years repeat in a 28-year cycle (1461 weeks). Each leap-year dominical letter occurs exactly once and every common letter thrice.
The final two digits of Julian years repeat after 700 years, i.e. 25 cycles. When starting to count in 2001 for instance, every 5th, 11th and 22nd year of these Julian cycles is a common year that starts on a Saturday, i.e. ca. 10.71 % of all years. They are always 6 or 11 years apart.