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.