Hello, yosso!

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 . . .