On Ducci sequences with primes

Mihai Caragiu, Alexandru Zaharescu, Mohammad Zaki

Research output: Contribution to journalArticlepeer-review

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,P2,....,Pd) into (gpf(p1 + P 2),gpf(P2+P3),-,gpf(pd+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 Po:= {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 languageEnglish (US)
Pages (from-to)32-38
Number of pages7
JournalFibonacci Quarterly
Volume52
Issue number1
StatePublished - 2014

ASJC Scopus subject areas

  • Algebra and Number Theory

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