## Abstract

We introduce an analogue of the Ducci game that involves d-tuples of prime numbers subjected to the iteration G sending such a d-tuple (p _{1},P_{2},....,P_{d}) into (gpf(p_{1} + P _{2}),gpf(P_{2}+P_{3}),-,gpf(p_{d}+P _{1})), where for any x ≥ 1, gpf(x) represents the greatest prime factor of the integer x. We show that the iteration of G always leads into a limit cycle C. Moreover, if C has length greater than 1, then not only every vector in C has all components in P_{o}:= {2,3,5,7}, but every element of Po appears as a component of some vector in C. An analysis of the lengths of the nontrivial cycles for small values of d is provided.

Original language | English (US) |
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Pages (from-to) | 32-38 |

Number of pages | 7 |

Journal | Fibonacci Quarterly |

Volume | 52 |

Issue number | 1 |

State | Published - 2014 |

## ASJC Scopus subject areas

- Algebra and Number Theory