An Activation-Code Sequence

Consider the sequence $1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,\dots$, where the first term is $2^0$, the next two terms are $2^0,2^1$, the next three are $2^0,2^1,2^2$, and so on. Find the smallest integer $N>100$ such that the sum of the first $N$ terms of the sequence is a power of $2$.