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Search: id:A116369
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| A116369 |
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Day of the week corresponding to Jan 01 of a given year (n=0 for the year 2000) |
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+0
1
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| 7, 2, 3, 4, 5, 7, 1, 2, 3, 5, 6, 7, 1, 3, 4, 5, 6, 1, 2, 3, 4, 6, 7, 1, 2, 4, 5, 6, 7, 2, 3, 4, 5, 7, 1, 2, 3, 5, 6, 7, 1, 3, 4, 5, 6, 1, 2, 3, 4, 6, 7, 1, 2, 4, 5, 6, 7, 2, 3, 4, 5, 7, 1, 2, 3, 5, 6, 7, 1, 3, 4, 5, 6, 1, 2, 3, 4, 6, 7, 1, 2, 4, 5, 6, 7, 2, 3, 4, 5, 7, 1, 2, 3, 5, 6, 7, 1, 3, 4, 5, 6, 7, 1, 2, 3
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The number of days in the 400 year cycle of the Gregorian calendar is 365 * 400 + 100 (leap year every 4 years) - 4 (no leap year in centuries) + 1 (leap year every 400 yrs) = 146097 days. Since 146097 is (coincidentaly) divisible by 7 (7 * 20871), the cycle repeats exactly every 400 years. As a consequence, the probability of Jan 01 of a given year being any given weekday is not 1/7. Sunday, Tuesday and Friday have the highest probability (14.50%) Wednesday and Thursday: 14.25% Monday and Saturday: 14.00%
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REFERENCES
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N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
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LINKS
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N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site
PandaWave Company, World Calendars
E. G. Richards, Mapping Time, The Calendar and its History, Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, Reprinted 1999 (with corrections) page 231-5, 290, 311, 321.
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FORMULA
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1 = Sunday, 2 = Monday, 3 = Tuesday, 4 = Wednesday, 5 = Thursday, 6 = Friday and 7 = Saturday. a(n+400) = a(n) since the cycle repeats every 400 years.
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EXAMPLE
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E.g. a(6) = 1 because Jan 01 2006 was a Sunday.
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MATHEMATICA
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(* first do *) Needs["Miscellaneous`Calendar`"] (* then *) Table[DayOfWeek[{2000 + n, 1, 1}], {n, 0, 104}] /. {Sunday -> 1, Monday -> 2, Tuesday -> 3, Wednesday -> 4, Thursday -> 5, Friday -> 6, Saturday -> 7} - Robert G. Wilson v (rgwv(at)rgwv.com), Apr 04 2006
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CROSSREFS
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Cf. A060512, A053401, A101944.
Adjacent sequences: A116366 A116367 A116368 this_sequence A116370 A116371 A116372
Sequence in context: A126341 A078087 A021857 this_sequence A092234 A065476 A019945
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KEYWORD
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nonn
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AUTHOR
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Sergio Pimentel (ferdiego(AT)cox.net), Mar 15 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 04 2006
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