ePrint Report: On the gap between terms in an addition chain
Theophilus Agama
In this paper, we study the distribution of the textit{gap} between terms in an addition chain. In particular, we show that if $1,2,ldots,s_{delta(n)}=n$ is an addition chain of length $delta(n)$ leading to $n$, then $$underset{1leq lleq delta(n)}{mathrm{sup}}(s_{l+k}-s_l)gg kfrac{n}{delta(n)}$$ and $$underset{1leq lleq delta(n)}{mathrm{inf}}(s_{l+k}-s_l)ll kfrac{n}{delta(n)}$$ for fixed $kgeq 1$.