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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/unesp/360836
Title: 
Prime-generating recurrence
Author(s): 
Rowland, Eric
Language: 
eng
Description: 
  • This Demonstration explores solutions of the recurrence a(n)=a(n-1)+gdc(n,a(n-1)) through the difference sequence a(n)-a(n-1), which exhibits complex behavior. For the initial condition a(1)=7, the sequence a(n)-a(n-1) consists entirely of 1s and primes, making this recurrence a rare "naturally occurring" generator of primes. This result is not true in general: for example, letting a(1)=800 produces a(21)-a(20)=21, and letting produces . However, for these initial conditions, the difference sequence eventually consists entirely of 1s and primes. It is an unsolved problem to determine whether all initial conditions eventually produce only 1s and primes. You can choose to view all terms of the difference sequence or only the terms which are not 1
  • Prime Numbers
  • Componente Curricular::Ensino Fundamental::Séries Finais::Matemática
Issue Date: 
  • 2008
  • 15-Sep-2008
  • 15-Sep-2008
  • 15-Sep-2008
  • 12-Sep-2008
Keywords: 
  • Prime Numbers
  • Discrete Mathematics
  • Number Theory
  • Educação Básica::Ensino Fundamental Final::Matemática::Números e operações
Notes: 
Show the prime-generating recurrence
Credits: 
This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Source: 
http://objetoseducacionais2.mec.gov.br/handle/mec/5292
URI: 
http://acervodigital.unesp.br/handle/unesp/360836
Rights: 
Demonstration freeware using Mathematica Player
Type: 
outro
Appears in Collections:MEC - Objetos Educacionais (BIOE) - OE

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