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

0,1

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%.

References

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

Links

Table of n, a(n) for n=0..104.

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

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.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A060512, A053401, A101944.

Sequence in context: A021857 A222224 A163333 * A155751 A092234 A160101

Adjacent sequences: A116366 A116367 A116368 * A116370 A116371 A116372

Keyword

nonn

Author

Sergio Pimentel, Mar 15 2006

Extensions

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

Status

approved