Solve sequence for a promo code!

There's a game called Alice on the Run and the designer prices it as $1. However, to meet the people who don't want to pay any money for it, he writes a problem whose answer is a promo code and whoever gets it correct can get the game for free.

The problem is as follows:

Given a sequence $1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,...$ (See A059268 ) , where the first term is $2^0$ , the next two terms are $2^0,2^1$ , the next three terms are $2^0,2^1,2^2$ , etc.

The promo code is the smallest integer $N$ such that $N>100$ and the sum of first $N$ terms is an integer power of $2$ .

Find the promo code of the game.