Quite a simple question, I reckon, however, even quite an extensive search hasn't helped me.
I want to define a recursively defined sequence that starts with defined
f and distinguishes the input like so:
f[3k+2]. Each of these would have its own expression.
For further clarification, an example:
$$ f(3n) = f(n)+1 $$
$$ f(3n+1) = f(n)+2 $$
$$ f(3n+2) = f(n)+3 $$
How does one go about that? I do know how to write simple recursion formulas on the level of Fibonacci or a factorial, it's only the distinguishing the input part. Also, this should be possible without any
if statements, etc.
Thanks for any help!