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 $m\eq n$ . 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.

单词	AdditionChain
释义	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 $m\eq n$ . 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.
随便看	CubeOfAnInteger cube of an integer CubeOfANumber cube of a number CubeRoot cube root CubicallyThinHomotopy cubically thin homotopy CubicFormula cubic formula CubicReciprocityLaw cubic reciprocity law CubicSplineInterpolation cubic spline interpolation CullenNumber Cullen number CullenPrime Cullen prime CullinaneDiamondTheorem Cullinane diamond theorem CumulantGeneratingFunction cumulant generating function CumulativeDistributionFunction cumulative distribution function CumulativeHierarchy