The Prime-Power Map
Business Mathematics Department
School of Applied STEM
Universitas Prasetiya Mulya
South Tangerang 15339
Department of Mathematics
Parahyangan Catholic University
We introduce a modification of Pillai's prime map: the prime-power
map. This map fixes 1, divides its argument by p if it is a prime power
pk, and otherwise subtracts from its argument the largest prime power
not exceeding it. We study the iteration of this map over the positive
integers, developing, firstly, results parallel to those known for the
prime map. Subsequently, we compare its dynamical properties to those
of a more manageable variant of the map under which any orbit admits an
explicit description. Finally, we present some experimental observations,
based on which we conjecture that almost every orbit of the prime-power
map contains no prime power.
Full version: pdf,
(Concerned with sequences
Received October 12 2020; revised versions received December 28 2020; January 6 2021.
Published in Journal of Integer Sequences,
January 24 2021.
Journal of Integer Sequences home page