>   >>> a = var('a')
>   >>> assume(a, 'integer')
>   >>> integrate(2^2^floor(x), (x, a, a+1))
>   2^(2^a)
>
> Now you just need the summation of that over the range of integer
> intervals you are interested in but Sage's sum can't do anything with
> that and I'm not sure if anything else can either.
>

Thanks. I expected the definite integral to give solution.

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