Common year where year divided by 4 has a remainder of 1

A common year that has a remainder of 1 when divided by 4 is a type of common year. The current year 2021 is an example of one. The previous such common year was 2017 and the next one will be 2025. With the exception of end-of-century common years, this common year corresponds entirely to the year that is 6 years after it. The last occurrence of the first two months of the year was 5 years before it and the last occurrence of the other 10 months was 11 years before it. For instance, all the months of 2021 will occur again in 2027. The last occurrence of the first 2 months and the last 10 months of 2021 were in 2016 and 2010, respectively.
Examples
*2001 (Common year starting on Monday)
*2005 (Common year starting on Saturday)
*2009 (Common year starting on Thursday)
*2013 (Common year starting on Tuesday)
*2017 (Common year starting on Sunday)
*2021 (Common year starting on Friday)
*2025 (Common year starting on Wednesday)
 
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