Intervals between Successive Friday 13ths

I worked out these intervals to be:

Interval  Months Weeks  Type   Leapday

Jan-Oct      9     39    3Q       no
Jan-Apr      3     13     Q       Yes
Feb-Mar      1      4     M       n
Feb-Aug      6     26    2Q       Y
Mar-Nov      8     35    3Q-M     -
Apr-Jul      3     13     Q       -
May-Jan      8     35    3Q-M     -
Jun-Feb      8     35    3Q-M     -
Jul-Sep +   14     61    5Q-M     n
Jul-Jun     11     48    4Q-M     Y
Aug-May      9     39    3Q       n
Aug-Oct +   14     61    5Q-M     Y
Sep-Dec      3     13     Q       -
Oct-Apr      6     26    2Q       n
Oct-Sep     11     48    4Q-M     Y
Nov-Aug      9     39    3Q       n
Nov-May      6     26    2Q       Y
Dec-Jun      6     26    2Q       n     
Dec-Mar      3     13     Q       Y

An interval marked '+' is more than a year long.

I classified the interval of 1 month = 4 weeks as M and the interval of 3 months = 13 weeks as Q. All the other types are made from adding or subtracting these two types as shown in the type column (e.g. 3Q-M is three Qs less an M).

There are 7 types of interval:

M, Q, 2Q, 3Q-M, 3Q, 4Q-M and 5Q-M
of which
Q, 2Q and 5Q-M may or may not contain a leap day.

M, 3Q-M and 3Q never contain a leap day and

4Q-M always contains a leap day.

Karl Palmen

Fri 13 December 2002