Draft of 2-adic Valuation Trees for Natural Numbers in the Visualization of Hexagon

Objectives: This article discovers the 2-adic valuation trees for natural numbers arranged in a hexagonal shape, which provides specific patterns. Methods: The natural numbers are arranged in the form of hexagon and 2-adic valuation trees are constructed by calculating 2-adic valuations for special patterns of numbers presented in the above arrangement with the help of the property of congruence. Findings: Creation of a comprehensive formation of the valuation tree produced for the 2-adic valuation of the above declared sequences. Novelty: Generating 2-adic valuation trees for natural numbers are visualized in the shape of a hexagon is an original contribution, providing a new way to understand the relationships and structures within these sequences. Keywords: 2-adic valuation, Hexagonal number, Prime factorization, Congruence, Binary tree