Algo: Time Complexity closed

Question

What is the time complexity of the following piece of code in the terms of n?

$Main()$
{
$n=2^{2^k};$
$for(i=1; i<=n; i++)$
{
     $j=2;$
    $while(j<=n)$
   {
     $j=j^2;$
   }
}
}

Comments

Loop will run for $n*(k+1)$ time and $k=loglogn$ hence overall TC will be $O(nloglogn)$.

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i dont think you are correct

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Inner loop  

while(j<=n)

will run $k+1$ times for every itteration of  outer loop

explanation-:

sequence of inner loop will be 

$2^{1},2^{2},2^{4}....2^{2^{k}}$

hence it is running for $k+1$ times.

Outer loop will run $n=2^{2^{k}}$ times.

Hence total time complexity=$n=2^{2^{k}} \times k+1 \approx O(2^{2^{k}})$

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Take the value of K =2. So n=16. Outer loop will run 16 times.

Inner loop will run for value J=2,4 and 16(3 times).

So overall time=n*[loglog(n)+1]=n(K+1)