A game with divisors and absolute differences of exponents

Cristian Cobeli, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we discuss a number game that develops in a manner similar to that on which Gilbreath's conjecture on iterated absolute differences between consecutive primes is formulated. In our case the action occurs at the exponent level and there, the evolution is reminiscent of that in a final Ducci game. We present features of the whole field of the game created by the successive generations, prove an analogue of Gilbreath's conjecture and raise some open questions.

Original languageEnglish (US)
Pages (from-to)1489-1501
Number of pages13
JournalJournal of Difference Equations and Applications
Volume20
Issue number11
DOIs
StatePublished - Nov 26 2014

Keywords

  • Ducci game
  • Gilbreath's conjecture
  • Sierpinski triangle
  • absolute differences
  • primes game

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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