Integers with a small number of minimal addition chains (Q1301847)

A sequence \(A(n)=(a_0<a_1<\dots<a_r=n)\) of integers is called an addition chain if every term of it---except the first---is the sum of two preceding terms of the chain. An addition chain \(A(n)\) is called a minimal addition chain if its length is minimal. The author proves that a minimal addition chain \(A(n)\) is unique if and only if \(n=3\) or \(n=2^k\). Furthermore all \(n\) are characterized for which there are exactly two minimal addition chains.