addition chain

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.

Title	addition chain
Canonical name	AdditionChain
Date of creation	2013-03-22 18:27:27
Last modified on	2013-03-22 18:27:27
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11B13