Integers with a small number of minimal addition chains
type: Item
instance of: scholarly article
title: Integers with a small number of minimal addition chains
zbMATH Open document ID: 0945.05007
DOI: 10.1016/S0012-365X(99)00103-X
author: Achim Flammenkamp
published in: Discrete Mathematics
publication date: 2000-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 1334690
zbMATH Keywords: minimal addition chains
reviewed by: Norbert Hegyvári
MaRDI profile type: Publication
cites work: Q3935355
cites work: Addition chains -- an erratic sequence
description: scientific article; zbMATH DE number 1334690