1998 Calendar Jan-Jun

 Jan Feb Mar Apr May Jun 5 1 1 4 6 2 6 2 2 5 0 3 0 3 3 6 1 4 1 4 4 0 2 5 2 5 5 1 3 6 3 6 6 2 4 0 4 0 0 3 5 1 5 1 1 4 6 2 6 2 2 5 0 3 0 3 3 6 1 4 1 4 4 0 2 5 2 5 5 1 3 6 3 6 6 2 4 0 4 0 0 3 5 1 5 1 1 4 6 2 6 2 2 5 0 3 0 3 3 6 1 4 1 4 4 0 2 5 2 5 5 1 3 6 3 6 6 2 4 0 4 0 0 3 5 1 5 1 1 4 6 2 6 2 2 5 0 3 0 3 3 6 1 4 1 4 4 0 2 5 2 5 5 1 3 6 3 6 6 2 4 0 4 0 0 3 5 1 5 1 4 6 2 6 2 5 0 3 0 3 1

Months of January to June from 1998 calendar are shown in mod 7 for the dates.  This year had a start day of Thursday.   Refer to the non leap year table to see that the table and this calendar match on the Fridays that are the 13th.  The second table has the last six months of the year.  Any year that is a non leap year with the start date of Thursday will have the same results.  This table was made with Excel and used the formula feature to calculate the mod 7 entries.

1998 Calendar Jul – Dec

 Jul Aug Sep Oct Nov Dec 4 0 3 5 1 3 5 1 4 6 2 4 6 2 5 0 3 5 0 3 6 1 4 6 1 4 0 2 5 0 2 5 1 3 6 1 3 6 2 4 0 2 4 0 3 5 1 3 5 1 4 6 2 4 6 2 5 0 3 5 0 3 6 1 4 6 1 4 0 2 5 0 2 5 1 3 6 1 3 6 2 4 0 2 4 0 3 5 1 3 5 1 4 6 2 4 6 2 5 0 3 5 0 3 6 1 4 6 1 4 0 2 5 0 2 5 1 3 6 1 3 6 2 4 0 2 4 0 3 5 1 3 5 1 4 6 2 4 6 2 5 0 3 5 0 3 6 1 4 6 1 4 0 2 5 0 2 5 1 3 6 1 3 6 2 4 0 2 4 0 3 5 1 3 5 1 4 6 2 4 6 2 0 5

By using the table below, we can determine if there is a pattern that can be used to predict when the next time that there will be back to back months that contain a Friday the 13th.  This table was started from the year 1998.  Each year that was non leap year results in a start day of plus one.  For example if January 1 was on Thursday on the current year, then on the next year January 1 will be on Friday.  On the year following a leap year the start day will be plus two.  So after a leap year, if the starting date had been Saturday, the next year’s starting date will be Monday.

Back to Back Months of Friday the 13th by Year

 Year Leap Feb Mar Year Leap Feb Mar 1998 y y 2029 1999 2030 2000 y 2031 2001 2032 y y 2002 2033 2003 2034 2004 y y 2035 2005 2036 y 2006 2037 y y 2007 2038 2008 y 2039 2009 y y 2040 y 2010 2041 2011 2042 2012 y 2043 y y 2013 2044 y 2014 2045 2015 y y 2046 2016 y 2047 2017 2048 y 2018 2049 2019 2050 2020 y 2051 2021 2052 y 2022 2053 2023 2054 y y 2024 y 2055 2025 2056 y 2026 y y 2057 2027 2058 2028 y 2059

We can see from our previous analysis that a start day of Thursday will result in the back to back Friday the 13th in February and March.  If we let this start date be represented by x and add 1 to that start date for each non leap year and add 2 to that start date for the leap year, then we will by mod 7 at the next Thursday start day in 2004, but since this is a leap year only February will have Friday the 13th and not March.  Continuing with this process the next back to back will occur in 2009.  We know that this is the case, since it has already occurred.  If this analysis is continued it would appear that the pattern to arriving at years that have a back to back Friday the 13th in February and March happens in a pattern of two eleven year periods followed by a six year period and then repeats again.  Thus, the next year that this will occur is in 2015, followed by 2026, 2037, 2043, 2054, 2065, 2071, 2082, 2093, and 2099.