A053401 -id:A053401 - 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

A375666 Number of seconds in time units: second, minute, hour, day, week, month, year, decade, century, millennium, eon (in Julian years).

Original entry on oeis.org

1, 60, 3600, 86400, 604800, 2629800, 31557600, 315576000, 3155760000, 31557600000, 31557600000000000

Offset: 1

Robert B Fowler, Aug 23 2024

The last six numbers are based on the average Julian calendar year of 365.25 days, which appears frequently in astronomical publications, where it is usually called simply "Julian years".

UnitJuggler, Convert julian years (average) to milliseconds

Cf. A053401 (with Gregorian years of 365.2425 days).

Cf. A213612, A213613, A213614 (uses a(7)).

A375862 Number of caesium clock "ticks" in time units: tick, second, minute, hour, day, week, month, year, decade, century, millennium, eon (in Julian years).

Original entry on oeis.org

1, 9192631770, 551557906200, 33093474372000, 794243384928000, 5559703694496000, 24174783028746000, 290097396344952000, 2900973963449520000, 29009739634495200000, 290097396344952000000, 290097396344952000000000000

Offset: 1

Robert B Fowler, Aug 31 2024

The standard SI second has been defined since 1968 as 9192631770 (A230458) transitions ("ticks") of the caesium-133 atom.

The values of a(7) to a(12) are based on the average Julian calendar year of 365.25 days, which appears frequently in astronomical publications, where it is usually called simply "Julian years".

Wikipedia, Atomic clock.

Cf. A053401, A375666 (similar sequences based on units of seconds).
Cf. A213612, A213613, A213614 (use seconds in year).
Cf. A230458 (value of a(2)).

a(n) = A375666(n-1) * 9192631770, n>1.

cp's OEIS Frontend

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

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A375666 Number of seconds in time units: second, minute, hour, day, week, month, year, decade, century, millennium, eon (in Julian years).

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Author

Keywords

Comments

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A375862 Number of caesium clock "ticks" in time units: tick, second, minute, hour, day, week, month, year, decade, century, millennium, eon (in Julian years).

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Author

Keywords

Comments

Links

Crossrefs

Formula