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Indices of distinct Gregorian calendar year types in a 400-year period, indexed in order of occurrence in the 3rd millennium CE.
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%I #46 Jan 12 2021 01:24:17

%S 1,2,3,4,5,6,1,7,8,9,5,10,2,3,8,11,6,1,2,12,9,5,6,13,3,8,9,14,1,2,3,4,

%T 5,6,1,7,8,9,5,10,2,3,8,11,6,1,2,12,9,5,6,13,3,8,9,14,1,2,3,4,5,6,1,7,

%U 8,9,5,10,2,3,8,11,6,1,2,12,9,5,6,13,3,8,9,14

%N Indices of distinct Gregorian calendar year types in a 400-year period, indexed in order of occurrence in the 3rd millennium CE.

%C The 3rd millennium CE began with the year 2001 CE.

%C There are 14 distinct Gregorian calendar year types, since a year may begin on any day of the week and it may or may not be a leap year.

%C This sequence has a period of 400 years because the sequence of leap years in the Gregorian calendar has a period of 400 years and the number of days in this 400-year period (146097) is a multiple of 7.

%C This sequence has an underlying cycle of 28 years that begins on the first year of a century and is disrupted by the last year of the century, except the century leap year.

%C All 14 calendar year types occur at least once in a 28-year cycle.

%C The shortest period that includes all 14 calendar year types is 25 years long (e.g., a(4) - a(28)). There are 79 such distinct periods.

%C The longest period that does not include all 14 calendar year types is 39 years long (e.g., a(65) - a(103)). There are 27 such distinct periods.

%C The 14 calendar year types occur with the following frequencies over a 400-year period: 43, 44, 43, 13, 43, 43, 14, 44, 43, 15, 15, 14, 13, 13.

%H Ehit Dinesh Agarwal, <a href="/A339738/b339738.txt">Table of n, a(n) for n = 1..400</a>

%H <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>

%e a(1) = 1 since 2001 CE is the first year of the 3rd millennium CE.

%e a(7) = 1 since 2007 CE, like 2001 CE, is not a leap year and begins on a Monday.

%e a(99) = 8; the 28-year cycle is disrupted after a(15).

%e a(100) = 9, instead of 11, since 2100 CE is not a leap year.

%e a(101) = 5; the 28-year cycle begins at a(5).

%e a(199) = 2; the 28-year cycle is disrupted after a(19).

%e a(200) = 3, instead of 12, since 2200 CE is not a leap year.

%e a(201) = 8; the 28-year cycle begins at a(9).

%e a(299) = 6; the 28-year cycle is disrupted after a(23).

%e a(300) = 1, instead of 13, since 2300 CE is not a leap year.

%e a(301) = 2; the 28-year cycle begins at a(13).

%e a(4)-a(28) is the shortest period that includes all 14 calendar year types.

%e a(65)-a(103) is the longest period that does not include all 14 calendar year types.

%Y Cf. A127376.

%K nonn

%O 1,2

%A _Ehit Dinesh Agarwal_, Jan 05 2021