Pumping Lemma On Context Free Language

Question

For the language {a^2^n | n >= 0}

I understand that first some k is chosen, and then z = uvwxy such that vx != epsilon and #(vwx) <= k, but I can't think of any i which proves that this language is not context free.

Answer 1

Here's a hint: if you consider any power of two greater than k (say, 2^k), then 2^k + k is not a power of two, since

2^k + k < 2^k + 2^k = 2^k+1

See if that can guide you to choose the right string and find your choice of i.

Hope this helps!