{ "abstract": "An addition chain of length $h$ that leads to a number $n$ is a strictly increasing sequence of positive integers $s_0=1,s_1=2,\\ldots,s_h=n$ such that $s_i=s_j+s_k$~($i>j\\geq k$) for each $1\\leq i\\leq h$. The \\emph{Brauer} addition chain is the one where $j=i-1$ for each $1\\leq i\\leq h$. Let $\\ell(\\cdot)$ denote the minimal length of an addition chain that leads to an integer $\\cdot$. We say that step $i$ is \\emph{Brauer} when $j=i-1$. Similarly, we say that step $i$ is \\emph{non-Brauer} when $j