Journal of Integer Sequences, Vol. 24 (2021), Article 21.6.1

2-Adic Valuations of Quadratic Sequences


Will Boultinghouse
Kentucky Wesleyan College
Division of Natural Sciences and Mathematics
3000 Frederica Street
Owensboro, KY 42301
USA

Jane Long
Stephen F. Austin State University
Department of Mathematics and Statistics
Nacogdoches, TX 75962-3040
USA

Olena Kozhushkina
Ursinus College
Department of Mathematics and Computer Science
Collegeville, PA 19426
USA

Justin Trulen
Kentucky Wesleyan College
Division of Natural Sciences and Mathematics
3000 Frederica Street
Owensboro, KY 42301
USA

Abstract:

We determine properties of the 2-adic valuation sequences for general quadratic polynomials with integer coefficients directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.

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Received June 15 2020; revised versions received June 30 2020; March 12 2021; May 5 2021; May 14 2021. Published in Journal of Integer Sequences, May 17 2021.

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