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.