I don't have a complete solution yet,
. . but I have some ideas . . .
How could I construct a function which relate an argument and a value this way?
This is obviously periodic function, so I can write: .
but how could I give a comprehensive formula for ?
Should I write piecewise definition, or recursive, or ... ?
We can describe the first "cycle" with this function:
We can also describe the first cycle with a piecewise function:
Either way, we must make it cyclic with a period of 12.
Hmmm . . .