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A339738 Indices of distinct Gregorian calendar year types in a 400-year period, indexed in order of occurrence in the 3rd millennium CE.

%I A339738 #46 Jan 12 2021 01:24:17
%S A339738 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 A339738 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 A339738 8,9,5,10,2,3,8,11,6,1,2,12,9,5,6,13,3,8,9,14
%N A339738 Indices of distinct Gregorian calendar year types in a 400-year period, indexed in order of occurrence in the 3rd millennium CE.
%C A339738 The 3rd millennium CE began with the year 2001 CE.
%C A339738 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 A339738 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 A339738 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 A339738 All 14 calendar year types occur at least once in a 28-year cycle.
%C A339738 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 A339738 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 A339738 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 A339738 Ehit Dinesh Agarwal, <a href="/A339738/b339738.txt">Table of n, a(n) for n = 1..400</a>
%H A339738 <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>
%e A339738 a(1) = 1 since 2001 CE is the first year of the 3rd millennium CE.
%e A339738 a(7) = 1 since 2007 CE, like 2001 CE, is not a leap year and begins on a Monday.
%e A339738 a(99) = 8; the 28-year cycle is disrupted after a(15).
%e A339738 a(100) = 9, instead of 11, since 2100 CE is not a leap year.
%e A339738 a(101) = 5; the 28-year cycle begins at a(5).
%e A339738 a(199) = 2; the 28-year cycle is disrupted after a(19).
%e A339738 a(200) = 3, instead of 12, since 2200 CE is not a leap year.
%e A339738 a(201) = 8; the 28-year cycle begins at a(9).
%e A339738 a(299) = 6; the 28-year cycle is disrupted after a(23).
%e A339738 a(300) = 1, instead of 13, since 2300 CE is not a leap year.
%e A339738 a(301) = 2; the 28-year cycle begins at a(13).
%e A339738 a(4)-a(28) is the shortest period that includes all 14 calendar year types.
%e A339738 a(65)-a(103) is the longest period that does not include all 14 calendar year types.
%Y A339738 Cf. A127376.
%K A339738 nonn
%O A339738 1,2
%A A339738 _Ehit Dinesh Agarwal_, Jan 05 2021