4 times every 28 years, on the pattern 6 years - then 5 years - then 6 years - then 11 years. [This does not account for non-leap century years, such as 1900 and 2100, which disrupt the pattern.]
In specific years, it happened in 1977, 1983, 1988, 1994, 2005 and 2011. The next two occurrences will be in 2016 and 2022.
As of 2011, October 1 will next fall on Saturday in 2016.
Saturday
14
Saturday Night Live premiered on October 11, 1975.
2016, 2022, 2033, 2039, 2044, 2050, 2061, 2067, ...
January 1, will next fall on a Saturday in 2011.
As a general rule, July 1 falls on a Saturday every 6.981481481 years. Given rounding, you can, therefore, say July 1 falls on a Saturday once every 7 years.
March 1 will next fall on a Saturday in 2014.
1 October 1983 was a Saturday.
1 October 2005 was a Saturday.
October 1 1949 was a Saturday.
The next time Dec. 1 will fall on a Saturday will be in 2018.