A101944 Number of months in a 400-year cycle that have the thirteenth day of the month fall on the n-th day of the week, beginning with Sunday.

687, 685, 685, 687, 684, 688, 684

Offset: 1

Author

Robert G. Wilson v, Jan 28 2005

Keywords

• fini
• full
• nonn
• dumb

Comments

Friday the thirteenth appears more often than any other day.

In the cycle of 400 Gregorian years there are 303 regular years with 365 days, and 97 leap years with 366 days, so the total number of days is 303*365 + 97*366 = 146097, which is divisible by 7. - Amiram Eldar, Apr 29 2022

References

• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 230.

Links

• E. G. Richards, Mapping Time, The Calendar and its History, Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, Reprinted 1999 (with corrections).
• Wikipedia, Gregorian calendar
• Index entries for sequences related to calendars

Programs

Mathematica

(* first do *) Needs["Miscellaneous`Calendar`"] (* then *) t = Flatten[ Table[ DayOfWeek[{y, m, 13}], {y, 2000, 2399}, {m, 12}]]; d = Table[ DayOfWeek[{2006, 1, d}], {d, 1, 7}]; Table[ Count[t, d[[n]]], {n, 1, 7}]