New Year Tables for 5:40:400 Rule
The 5:40:400 leapweek calendar has a leapweek on every year divisible by 5, except those divisible by 40, except those divisible by 400. Its cycle matches the Gregorian cycle, hence its New year repeats every 400 years, with respect to the Gregorian Calendar. The new years can be calculated using two tables each with 20 entries.
Below is such a pair of tables, where the new years match for 2001.
The first table gives the position of 5:40:400 New year relative to the Gregorian New year for the period 2001-2020
Table 1: 2001-20202001: same 2011: 2 days late 2002: 1 day early 2012: 1 day late 2003: 2 days early 2013: 1 day early 2004: 3 days early 2014: 2 days early 2005: 5 days early 2015: 3 days early 2006: 1 day late 2016: 3 days late 2007: same 2017: 1 day late 2008: 1 day early 2018: same 2009: 3 days early 2019: 1 day early 2010: 4 days early 2020: 2 days earlyThe new years for other 20 year periods follow the same pattern, but are displaced by a constant number of days as shown in Table 2.
Table 2: Other 20 year periodsExamples2021-2040 3 days later 2041-2060 1 day earlier 2061-2080 2 days later 2081-2100 2 days earlier 2101-2120 2 days later 2121-2140 2 days earlier 2141 2160 1 day later 2161-2180 3 days earlier 2181-2200 as 2001-2020 1801-1820 3 days earlier 1821-1840 as 2001-2020 1841-1860 4 days earlier 1861-1880 1 day earlier 1881-1900 5 days earlier 1901-1920 1 day earlier 1921-1940 5 days earlier 1941-1960 2 days earlier 1961-1980 6 days earlier 1981-2000 3 days earlierFor example 1999: table 1 year 2019: 1 day early table 2 1981-2000: 3 days earlier total: 4 days early (i.e. 28 Dec 1998). For example 2022: table 1 year 2002: 1 day early table 2 2021-2040: 3 days later total: 2 days late (i.e. 3 Jan 2022).The earliest new year is 1965 (11 days early), which is Monday 21 Dec 1964 and a Solstice day.
The latest new year is 2036 (6 days late) which is Monday 7 Jan 2036.
Copyright 2001 Karl Palmen
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