R = ((11 Y + 14) / 30)_r,
the year is intercalary when R < 11.
[v.04 p.1002] Also the number of intercalary years from the year 1 up to
the year Y inclusive = ((11 Y + 14) / 30)_w; and the same up to the year Y
- 1 = (11 Y + 3 / 30)_w.
To find the day of the week on which any year of the Hegira begins, we
observe that the year 1 began on a Friday, and that after every common year
of 354 days, or 50 weeks and 4 days, the day of the week must necessarily
become postponed 4 days, besides the additional day of each intercalary
year.
Hence if w = 1 | 2 | 3 | 4 | 5 | 6 | 7
indicate Sun. | Mon. | Tue. | Wed. | Thur. | Frid. | Sat.
the day of the week on which the year Y commences will be
w = 2 + 4(Y / 7)_r + ((11 Y + 3) / 30)_w (rejecting sevens).