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

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

Offset

1,2

Comments

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

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.

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.

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.

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

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.

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.

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.

Links

Ehit Dinesh Agarwal, Table of n, a(n) for n = 1..400

Index entries for sequences related to calendars

Example

a(1) = 1 since 2001 CE is the first year of the 3rd millennium CE.
a(7) = 1 since 2007 CE, like 2001 CE, is not a leap year and begins on a Monday.
a(99) = 8; the 28-year cycle is disrupted after a(15).
a(100) = 9, instead of 11, since 2100 CE is not a leap year.
a(101) = 5; the 28-year cycle begins at a(5).
a(199) = 2; the 28-year cycle is disrupted after a(19).
a(200) = 3, instead of 12, since 2200 CE is not a leap year.
a(201) = 8; the 28-year cycle begins at a(9).
a(299) = 6; the 28-year cycle is disrupted after a(23).
a(300) = 1, instead of 13, since 2300 CE is not a leap year.
a(301) = 2; the 28-year cycle begins at a(13).
a(4)-a(28) is the shortest period that includes all 14 calendar year types.
a(65)-a(103) is the longest period that does not include all 14 calendar year types.

Crossrefs

Cf. A127376.

Sequence in context: A243733 A334618 A138776 * A364500 A280701 A064830

Adjacent sequences: A339735 A339736 A339737 * A339739 A339740 A339741

Keyword

nonn

Author

Ehit Dinesh Agarwal, Jan 05 2021

Status

approved