5515-Year Luni-Solar Cycle

5515-Year Luni-Solar Cycle

Here's the decomposition is smaller, more well-known cycles;
5515 years = 166*( 33 years ) + 37 years
5515 years = 7*( 334 years ) + 9*( 353 years )

The cycle of entirety
= 4173 yerms
= 5515 years
= 68211 months
= 154947 trecena
= 2014311 days

Mean year = 365 & 1336 / 5515 days = 365.2422484 days
Mean month = 29 & 928  / 1749 days = 29.5305889 days
13-month years = 2031

For a month count M and year count Y...

A luni-solar year has 13 months if
( 2031*Y + 2757 )MOD( 5515 ) < 2031

An ecclesiastical month has 30 days if
( 928*M + 874 )MOD( 1749 ) < 928

A month is a new year's month if
( 5515*M + 65453 )MOD( 68211 ) < 5515