# big o notation – What is the complexity of \$i^i\$?

What is the complexity of the following algorithm in Big O:

``````for(int i = 2; i < n; i = i^i)
{
...do somthing
}
``````

I’m not sure if there is a valid operator to this type of complexity.
My initial thought was as follows:

After $$k$$ iterations we want: (using tetration?)

$${^{k}i} = n implies k=logloglog…_klog{n}impliesmathcal{O(logloglog…_klog{n})}$$ (where we have k times the log function) but i’m not sure if this is evan a valid way of writing this.
Anyway, we have a complexity that that includes $$k$$, which does not seems right to me.