Divisibility Based Lexically Earliest Sequence with Cellular Automaton Behavior.

Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2024 0314.

Abstract.

We examine some qualities of a lexically earliest sequence (LES) based on divisibility of prime p that resemble a 1 dimensional cellular automaton that is affected by multiplication of a squarefree kernel r by kernel register m(r). The sequence moves into and out of “coherence”, defined in the paper, and in rare, intermittent, highly quasicoherent phases, admits primes and their perfect powers as well as composite powerful numbers. Otherwise the sequence is dominated by weak composites (as opposed to powerful numbers).

Click here for the PDF.

Concerns OEIS sequences:

A001694, A002110, A003586, A005117, A006530, A007947, A008578, A019565, A033845, A052485, A067255, A087207, A126706, A246547, A332785, A369609.

To cite:

Michael Thomas De Vlieger, Divisibility Based Lexically Earliest Sequence with Cellular Automaton Behavior, Simple Sequence Analysis, Article 20240314.