The 2-adic valuation of a sequence arising from a rational integral

TL;DR

This paper investigates the 2-adic valuations of a sequence derived from a quartic integral, offering a combinatorial interpretation and exploring links to the Collatz conjecture.

Contribution

It introduces a detailed analysis of the 2-adic valuations of a specific sequence and provides a novel combinatorial perspective, connecting it to the Collatz problem.

Findings

Characterization of 2-adic valuations of the sequence

Combinatorial interpretation of valuations

Connections to Collatz orbits

Abstract

We analyze properties of the 2-adic valuations of an integer sequence that originates from an explicit evaluation of a quartic integral. We also give a combinatorial interpretation of the valuations of this sequence. Connections with the orbits arising from the Collatz (3x+1) problem are discussed.