Journal of Integer Sequences, Vol. 24 (2021), Article 21.2.2

The Prime-Power Map

Business Mathematics Department
School of Applied STEM
Universitas Prasetiya Mulya
South Tangerang 15339

Jonathan Hoseana
Department of Mathematics
Parahyangan Catholic University
Bandung 40141


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.

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(Concerned with sequences A000040 A000079 A000961 A066352 A336825.)

Received October 12 2020; revised versions received December 28 2020; January 6 2021. Published in Journal of Integer Sequences, January 24 2021.

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