# Algorithms – What is the great complexity of time \$ O \$ of this nested loop for

I want the complexity of time to be great, oh $$Or$$ as well as the value of the count in terms of $$n$$

From my understanding,
the first for the cycle runs for $$lg (n)$$ times where $$lg (x) = log_2 (x)$$
Also, every time, $$i$$ it's the way $$2 ^ k$$ where $$; k en N cup {0 }$$ Y $$j$$ run from $$1$$ to $$i-1 = 2 ^ k -1 ; forall k en N cup {0 },$$ such that $$2 ^ k

Thus,
$$account = sum_ {k = 0} ^ {t} (2 ^ k – 1)$$ where $$2 ^ t geq n rightarrow t geq lg (n)$$. For the closest approximation to the count, take $$t = lg (n) ; text {{does this make sense?}}$$ Then we get:

$$count = sum_ {k = 0} ^ { lg (n)} (2 ^ {k} -1) = frac {1 times (2 ^ { lg (n)} – 1)} { 2-1} – ( lg (n) +1) = n- lg (n) -2$$. So is this $$O (n)$$?