This brief presentation will highlight the key ideas of the authors’ research diving into 2-adic valuations and their application to sequences: we look at lists of numbers that are created by certain rules (mathematically, these rules create a quadratic function). Then we ask at every position on these lists how many powers of two can be factored out. It is from this new list of numbers we try to find interesting properties. We use a program to arrange this list of numbers to generate a visual, which we call trees. The trees are composed of branches, and each branch represents a different collection of positions from the new list of numbers. Likewise, whether a branch splits into more branches is determined by what numbers are at those positions. We will discuss various patterns noticed in these trees and how they relate to the original rule of the quadratic function.
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