Patterned Dates

What & Why

These are lists of dates I have found which have numerical patterns in them. They are probably of no practical use at all but might be of occasional amusement as in "any excuse for a party" or "did you know your birthday this year has ...".

I got the idea when one of my friends joked in 2002 that a particular dance we were going to one evening was going encompass the time 8.02 pm on the 20th of February and therefore we could celebrate 2002 20-02 20:02!.

I wondered what other such dates could be found but not being so keen as to bother sifting through forthcoming dates myself I wrote a computer program to do it for me. It is not as versatile at recognising patterns as a human would be, of course, but it checks some basic pattern types with a thoroughness that would be too mind-numbing & time-consuming for a human to do. It certainly finds a lot of patterns in the dates!

Patterned Dates in the 20th Century

Choose the year: 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999.

Patterned Dates in the 21th Century

Choose the year: 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099.

Many more years with patterns

For other years in this & the previous millennium, the patterned dates from year 1000 to year 2999 are available as a compressed archive (7z format as it compresses this 4 times better than PK Zip or GZip). Size 429 KiB.

The program

For even more years, download my program for finding patterned dates (10 KiB). It is written in Perl and requires a Perl interpreter to run in. A Perl interpreter comes as standard on Linux & Mac OS X and is available for Microsoft Windows. See my article anent installing Perl scripts if you need more information. Run it in a console window and give one command line parameter (the year) to test dates in a single year or two command line parameters (the start & end years) to test the dates in a range of years.

Note that the number of patterns found varies tremendously with the degree of patterning in the year itself. E.g. it found nearly nine times as many in 2000 as it did in 1999 and thirty times as many as in 1974.

Date Formats Tested

  1. It tests 3 date orders: ISO (year-month-day); UK (day-month-year); and USA (month-year-day). Most other countries use orders like the ISO or UK one.
  2. It tests the year both in full (e.g. 2007) 2 digit (e.g. 07) form.
  3. It tests both with (e.g. March = 03) and without (e.g. March = 3) leading zeros.

It tests all combinations thereof (which can be up to 36 different representations of a single date!).

It does not take into account the separating characters (so it would spot that '2002-20-02' is a palindrome and a repeat despite the extra '-' in the second half).

It does not bother testing times of day as there so many times in each day that one can find early always easily contrive a time to match the date pattern.

(Personally, although I am from the UK, I prefer the ISO date order to the UK one because: it is logically consistent with most the way our 'Arabic' numbers & decimal quantities are written (highest place value on the left); it is consistent with how most non-decimal quantities are written (biggest units on the left as in hours-minutes-seconds & pounds-shillings-pence); it sorts alphanumerically into the chronological order; and it is a clearly defined international standard. However, even the UK date order is more logical than the muddled USA one.)

Patterns Tested

  1. Single digit: Where all the digits are the same. E.g. '2222-2-22'.
  2. Palindromes: Where reversing the digits leaves it unchanged. E.g. '2001-10-02'.
  3. Vertical mirror symmetry: Where flipping the number about its horizontal central line leaves it unchanged. The digits '1', '8' & '0' remain the same but and the other digits fail. E.g. '1880-01-18'.
  4. Horizontal mirror symmetry: Where flipping a number about its vertical central line leaves it unchanged. The digits reverse in order as in a palindrome, the digits '1', '8' & '0' remain the same, the digits '2' & '5' interchange and the other digits fail. E.g. '1580-08-21'.
  5. Ambigrams with diad (180 deg rotational) symmetry: Where rotating a number 180 deg about its centre in the plane of the page leaves it unchanged. The digits reverse in order as in a palindrome but '6' becomes '9', '9' becomes '6', '1', '8' & '0' stay the same and the other digits fail. E.g. '1060-09-01'.
  6. Cycling permutation symmetry: Where moving all the digits along some whole number of places (but less than the number of digits in the string) and putting any digits that fall off the end back on the beginning leaves it unchanged. Of course, this is equivalent to the number being composed of two or more repeating units. E.g. '1231-12-31' & '1981-9-8'.
  7. Arithmetic series: Where the number is composed of three or more substrings of digits with equal increments between them. E.g. '10-12-14' (increment of +2) & '2016-12-08' (increment of -4 when considered as '20', '16', '12' & '08').
  8. Geometric series with integral ratios: Where the number is composed of two or more substrings of digits with an integral ratio between them. E.g. '07-2-1' (ratio of 3 when considered as '07' & '21').

It also tests if there any patterns common to equal length substrings of digits in the number. E.g. '1969-19-11' is not a palindrome itself but in USA format with a two-digit year ('11-19-69') it can be split into two substrings ('111' & '969') both of which are palindromes.

Some inevitable duplicates are removed to save clutter in the list, e.g. arithmetic series of increment zero & geometric series of ratio 1 as they also have cyclic permutations symmetry and will so will already have been found.