Weird nested sequence! VijV_{ij}

Consider the sequence 3,18,243,...n×32n13,18,243,...n×3^{2^{n-1}}

If this sequence is enclosed in nested square roots upto infinite terms i.e. if

3+18+243+...=k\sqrt{3+\sqrt{18+\sqrt{243+...}}}=k,

Find the value of k\left\lceil{k}\right\rceil.

Note:

This problem is similar to the below problem.

Nested Radicals

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