Tricky sums indeed!

Let the function \(\Theta (n)\) denote the sum of all natural numbers less than or equal to \(n\). However, this function has one trick - if the number to be added \(i\) is a power of 2 (i.e \({ 2 }^{ x } \equiv i\)), then instead of adding, we subtract the number.

What is \(\displaystyle \sum _{ i=4 }^{ 10000 }{ \quad \Theta (i) } \)?

As an explicit example, \(\Theta (4) = -4\).

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