So I have a function
$f(x)=\left\{ \begin{array}{lr} 1, & x = 0 \\ 3 + f(x/2), & x = even \\ 3 + f((x-1)/2), & x = odd \end{array} \right.$
and I can see from graphing it, that it is approximately:
$f(x)=3\log_{2}(x) + 4$
where x > 0
what method(s) can I use to find this solution? Some kind of correlation? or is there an algebraic solution? or something else?
Problem source, incase I missed something: https://www.youtube.com/watch?v=Ud3oeInn_8c