Towers of 2

Define a sequence TkT_{k} such that T1=2{T_{1} = 2} and Tn=2Tn1{T_n = 2^{T_{n-1}}}.

Find the remainder when T1+T2+T3++T256{T_1 + T_2 + T_3 +\ldots + T_{256}} is divided by 255.

This is not an original problem.
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