Given integers d ≥ 1, and g ≥ 2, a g-addition chain for d is a sequence of integers The length of a g-addition chain is r, the number of terms following 1 in the sequence. We denote by l g (d) the length of a shortest addition chain for d. Many results have been established in the case g = 2. Our aim is to establish the same sort of results for arbitrary fixed g. In particular, we adapt methods for constructing g-addition chains when g = 2 to the case g > 2 and we study the asymptotic behavior of l g .
Yara Elias and Pierre McKenzie REF have established the results for arbitrary fixed g and adapted methods for constructing g-addition chains when g=2 to the case g>2.
On Generalized Addition Chains
INTEGERS, Volume 14, A16, 2014, http://www.integers-ejcnt.org/vol14.html
Mathematics Computer Science