TY - JOUR
T1 - On Ducci sequences with primes
AU - Caragiu, Mihai
AU - Zaharescu, Alexandru
AU - Zaki, Mohammad
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:84896911767
SN - 0015-0517
VL - 52
SP - 32
EP - 38
JO - Fibonacci Quarterly
JF - Fibonacci Quarterly
IS - 1
ER -