An addition chain $a$ is a sequence of integers of length $k$ such that each term $a_i$ for $0 < i \leq k$ (with $a_0 = 1$ is the sum of two previous terms in at least one way. In the sum $a_m + a_n$ it is not required that $m \neq n$ For example, 1, 2, 3, 5, 10, 20, 40, 80, is an addition chain of length 7: 3 is 1 + 2, 5 = 2 + 3, 10 = 5 + 5, and the rest have $m = n$

There are various subclassifications of addition chains, such as the Lucas chains. A Mian-Chowla sequence is an addition chain with the restriction that each term is the sum of two previous terms in only one way. The length may be infinite, and thus the Fibonacci sequence is an addition chain.