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Yeartypes[1] in relation to ISO weeknumbers
=================================================
(C) 1999-01-17, Magnus Bodin <magnus@bodin.org>
The #-numbers refers to ISO weeknumbers. What we can say for sure is that
yeartype {3,9,10} results with a week #53. We can also state that yeartypes
{0,1,2,3,7,8,9,10} starts with week #1, yeartypes {6,12} starts with week #52,
and yeartypes {4,11} starts with week #53. The yeartype {5} starts either
with #52 or #53 depending on if the preceeding year is of type {4} or {10}.
This results that only 57% of all years starts with week #1:
+----------+-----------+
|Startweek#| Frequency |
+----------+-----------+
| 1 | 57.00% |
+----------+-----------+
| 52 | 25.25% |
+----------+-----------+
| 53 | 17.75% |
+----------+-----------+
+----++------------------------------- ---------++-------------------
|year|| ||
|type|| Year n || Year n+1
+----++---------------------------+--- -----+---++-------------------
| ||#1 |#2 #52|#1
| 0 ||Mo |Tu |We |Th |Fr |Sa |Su |Mo |Su |Mo ||Tu |We |Th |Fr |Sa
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 |#1
| 1 ||Tu |We |Th |Fr |Sa |Su |Mo |Tu ... |Mo |Tu ||We |Th |Fr |Sa |Su
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 #1 |#2
| 2 ||We |Th |Fr |Sa |Su |Mo |Tu |We ... |Tu |We ||Th |Fr |Sa |Su |Mo
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 #53 |#1
| 3 ||Th |Fr |Sa |Su |Mo |Tu |We |Th ... |We |Th ||Fr |Sa |Su |Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#53 |#1 #52 |#1
| 4 ||Fr |Sa |Su |Mo |Tu |We |Th |Fr ... |Th |Fr ||Sa |Su |Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| || |#1 #52 |#1
| 5 ||Sa |Su |Mo |Tu |We |Th |Fr |Sa ... |Fr |Sa ||Su |Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#52|#1 #52 ||#1
| 6 ||Su |Mo |Tu |We |Th |Fr |Sa |Su ... |Sa |Su ||Mo |Tu |We |
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 |#1
| 7 ||Mo |Tu |We |Th |Fr |Sa |Su |Mo ... |Mo |Tu ||We |Th |Fr |Sa |Su
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 #1 |#2
| 8 ||Tu |We |Th |Fr |Sa |Su |Mo |Tu ... |Tu |We ||Th |Fr |Sa |Su |Mo
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 #53 |#1
| 9 ||We |Th |Fr |Sa |Su |Mo |Tu |We ... |We |Th ||Fr |Sa |Su |Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#1 |#2 #53 |#1
| 10 ||Th |Fr |Sa |Su |Mo |Tu |We |Th ... |Th |Fr ||Sa |Su |Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#53 |#1 #52 |#1
| 11 ||Fr |Sa |Su |Mo |Tu |We |Th |Fr ... |Fr |Sa ||Su |Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#52 |#1 #52 ||#1
| 12 ||Sa |Su |Mo |Tu |We |Th |Fr |Sa ... |Sa |Su ||Mo |Tu
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
| ||#52|#1 #52|#1
| 13 ||Su |Mo |Tu |We |Th |Fr |Sa |Su ... |Su |Mo ||Tu |We |Th |Fr |Sa
+----++---+---+---+---+---+---+---+--- -+---+---++---+---+---+---+---
--
[1] Our definition of yeartype is a numeric representation of what weekday
January 1st is and if the year is a leapyear or not. Like this:
+-------------+-------------------------------------------+
| weekday of | |
| January 1 | Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su |
+-------------+-------------------------------------------+
|year is leap?| X X X X X X X |
+-------------+-------------------------------------------+
| yeartype | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 |
+-------------+-------------------------------------------+
Read more on yeartypes and their distribution