Addition chains -- an erratic sequence (Q1313870)

An addition chain for a positive integer \(n\) is a set \(1=a_ 0<a_ 1< \cdots <a_ r=n\) of integers such that for \(i \geq 1\) \(a_ i=a_ j+a_ k\) for some \(k \leq j<i\). In this paper the function \(NMC(n)\) is considered; it is the number of chains for \(n\) with minimal \(r\). \(NMC(n)\) is determined for certain classes of integers; for some other integers lower bounds for \(NMC(n)\) are given.