1998 Calendar JanJun
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 13^{th}. 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 13^{th}. 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 13^{th} 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 13^{th} 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 13^{th} 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 13^{th} 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.