A060512 -id:A060512 - cp's OEIS frontend

A116369 Day of the week corresponding to Jan 01 of a given year (n=0 for the year 2000).

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

Offset: 0

Sergio Pimentel, Mar 15 2006

nonn

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 years) = 146097 days. Since 146097 is (coincidentally) 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%.

			a(6) = 1 because Jan 01 2006 was a Sunday.

N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.

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.
Index entries for sequences related to calendars

Cf. A060512, A053401, A101944.

(* 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, Apr 04 2006 *)

from datetime import date
def a(n): return (date(2000+n, 1, 1).isoweekday())%7 + 1
print([a(n) for n in range(105)]) # Michael S. Branicky, Jan 05 2021

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.

More terms from Robert G. Wilson v, Apr 04 2006

A060513 Number of units of time making up the next larger unit: seconds, minutes, hours, days, years, centuries, millennia.

Original entry on oeis.org

60, 60, 24, 365, 100, 10

Offset: 1

Philip Newton, Mar 23 2001

This assumes 365 days in a year, which is not exact. (All other conversions to next higher unit are exact.)

			The third term is 24 because there are 24 hours in one day.

Index entries for sequences related to calendars

Cf. A060512.

A116386 Number of calendar weeks in the year n (starting at n=0 for the year 2000).

Original entry on oeis.org

54, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53

Offset: 0

Sergio Pimentel, Mar 15 2006

Since 365/7 = 52.14 > 52, every year has at least 53 weeks (although the first and / or the last calendar weeks might not be complete and belong to two different years). Only if a leap year begins in a Saturday (the last day of the calendar week), a year can have 54 different calendar weeks (being the first and last of only one day). Years with 54 calendar weeks are: 2000, 2028, 2056, 2084, 2124, 2152, etc. It happens 13 times in a 400 year cycle.

			E.g. a(0)=54 because the year 2000 had 54 calendar weeks (since Jan 01 2000 was a Saturday and Dec 31 2000 was a Sunday)

Index entries for sequences related to calendars

Cf. A060512, A061251, A003786, A090651, A101312.

cp's OEIS Frontend

A112025 Duplicate of A060512.

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A116369 Day of the week corresponding to Jan 01 of a given year (n=0 for the year 2000).

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A060513 Number of units of time making up the next larger unit: seconds, minutes, hours, days, years, centuries, millennia.

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A116386 Number of calendar weeks in the year n (starting at n=0 for the year 2000).

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Author

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Comments

Examples

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Crossrefs