This picture represents 56 Lunar years.
On the Left side, you have the months, not twelve but 13 ( you can go here for an explanation on that) - The numbers highlighted in orange above all the numbers in blue, green and turquoise, are years.
This is an excel sheet I made - It represents 56 Lunar years and 693 months. All of those numbers in the blue, green and turquoise, represent Saturdays.
Within this you have an eclipse that will happen every 220 months, the first one on the
first day of the fourth month of the first year; 220 months later, it will be on the
first day of the second month of the nineteenth year.
My question regards finding an equation that will help me find the eclipses for a given
56 year cycle - let me explain more..
This image is
one 56 year cycle - each 56 year cycle has 3 eclipses max, because they happen every 18 solar years and 10 days OR
220 Lunar Months.
The pattern will always be offset until it resets at some point and starts over. What I mean by this, is that: each new 56 year cycle, the
first ecplipse for that cycle will be on a different day, until eventually, after $x$ amount of cycles (i think that number is $63$) it will 'reset', or start back over at the beginning, where the first eclipse for that 56 year cycle will be on the fourth month of the first year. (with this, i think it will be safe to say that we will have $63$ (for example) 56 year cycles... )
How, or where, can I begin to find a solution to this. I figured asking here would be my best option, because there are
A LOT of talented mathematicians here. Any help is appreciated.
If you would like further explanation, please ask - this all seems clear in my head, but I am not so sure it will be that clear in yours.