The Quadratic Distribution of Integers Relative to Squares and Oblongs

This study explores the application of quadratic distribution principles to the sequences odds and odds+2, and extends the analysis to odds±2k to uncover patterns that contribute to our understanding of number theory conjectures. By examining the behavior of quadratic sequences, particularly those derived from the difference between odd and even squares (and vice versa), we demonstrate that all odd composite numbers are distributed along the numerical line following specific quadratic patterns. This consistent reference to square and oblong numbers highlights the unique quadratic nature of odd composite number distributions. This discovery provides a new perspective on the intrinsic properties of these distributions, suggesting that such patterns can be predicted and modeled through quadratic formulas. These findings reinforce studies previously published in preprints, confirming, and expanding upon the established quadratic distribution principles observed in the distribution of odd composite numbers.