Code Library for the Sexagenary Cycle

https://en.wikipedia.org/wiki/Sexagenary_cycle

Code for converting between Gregorian and Chinese year numbers already exists. Wikipedia highlights the current year on the sexegenary cycle list, and somebody programmed that. But, all the same, I can amuse myself by thinking about it.

Things to be defined would include:

• the Ten Stems and the Twelve Branches
• the 60-element cycle formed from pairing Stems and Branches by the traditional method
• the 60-element "false cycle"¹, formed by all the pairs not in the traditional cycle
• given a number indicating 1 thru 60 as the starting year, and a number +/-N, return the Stem and Branch for the year N years after/before the starting year
• given a Gregorian year, return its Stem and Branch according to the traditional calendar
• given a Stem and Branch, return the most recent Gregorian year, or all of them (up to an optional stopping point), which were that Stem and Branch on the traditional calendar