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

Author

Sergio Pimentel, Mar 15 2006

Keywords

• nonn

Comments

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%.

Examples

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

References

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

Links

• 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

Crossrefs

Cf. A060512, A053401, A101944.

Programs

Mathematica

(* 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 *)

Python

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

Formula

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.

Extensions

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