Lucas chain

A Lucas chainMathworldPlanetmath a is an addition chainMathworldPlanetmath with the additional requirement that not only each term be the sum of two previous (not necessarily distinct) terms, but also that the difference of those two terms also be a term in the sequence. That is, each ai=am+an and also |an-am|=aj, with j being some nonnegative integer.

For example, the Fibonacci sequenceMathworldPlanetmath (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.) is a Lucas chain because not only is each term the sum of the previous two terms, each term is the difference of the next two terms. On the other hand, 1, 2, 4, 8, 9, 13, 21, 30, etc., is an addition chain but not a Lucas chain, since 8 + 13 = 21, but 13-8=5, which is not a member of the chain.

Title Lucas chain
Canonical name LucasChain
Date of creation 2013-03-22 18:29:22
Last modified on 2013-03-22 18:29:22
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11B13