mainly natural numbers - studies on sequences - h. ibstedt

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1、MainlyNaturalNumbers-afewelementarystudiesonSmarandachesequencesandothernumberproblemsHenryIbstedtThesurprisingbehaviourofasequenceAmericanResearchPressRehoboth,USA2003MainlyNaturalNumbers-afewelementarystudiesonSmarandachesequencesandothernumberproblemsHenryIbsted

2、tGlimminge20367,rueduSergentBlandan28060Broby92130IssylesMoulineauxSwedenFrancehibstedt@swipnet.sehibstedt@wanadoo.frAmericanResearchPressRehoboth,USA2003HenryIbstedt&AmericanResearchPressThediagramonthecoverillustratestheSmarandachepartialperfectadditivesequence.

3、Ithasanamusingoscillatingbehaviour,itdoesnotformloopsandhasnoterminatingvalue.Itsdefinitionissimplya1=a2=1,a2k+1=ak+1-1,a2k+2=ak+1+1Thisbookcanbeorderedinpaperboundformfrom:BooksonDemandProQuestInformation&Learning(UniversityofMicrofilmInternational)300N.ZeebRoadP.

4、O.Box1346,AnnArborMI48106-1346,USAhttp://www.lib.umi.com/bod/andonlinefrom:PublishingOnline,Co.(Seattle,WashingtonState)http://PublishingOnline.comPeerReviewers:D.Constantinescu,CollegeofArts,Rm.Vâlcea,Romania.M.Khoshnevisan,SchoolofAccountingandFinance,GriffithUni

5、versity,GoldCoast,Quensland9726,Australia.I.Prodan,KishinevUniversity,Kishinev,R.Moldova.Copyright2003byHenryIbstedt,Glimminge2036,28060Broby,Sweden.hibstedt@swipnet.seandAmericanResearchPress,Rehoboth,Box141,NM87322,USA.http://www.gallup.unm.edu/~smarandache/eBoo

6、ks-otherformats.htmISBN:1-931233-73-XStandardAddressNumber:297-5092PrintedintheUnitedStatesofAmericaPrefaceThisbookconsistsofaselectionofpapersmostofwhichwereproducedduringtheperiod1999-2002.TheyhavebeeninspiredbyquestionsraisedinrecentarticlesincurrentMathematicsj

7、ournalsandinFlorentinSmarandache’swellknownpublicationOnlyProblems,NotSolutions.Alltopicsareindependentofoneanotherandcanbereadseparately.Findingsareillustratedwithdiagramsandtables.Thelatterhavebeenkepttoaminimumasitisoftennotthenumbersbutthegeneralbehaviourandpat

8、ternofnumbersthatmatters.Oneofthefacinationswithnumberproblemsisthattheyareofteneasytoformulatebuthardtosolve–ifever,andifonefindsasolution,newqu