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Thoughts, ideas, and explorations

Welcome to My Blog

This is the first post on my blog. Here I'll share my thoughts about the absolute state of humanity, technology, hardcore research and other interesti...

Mathematical Analysis of XOR Sequences: Patterns and Properties

Let $S_n = \bigoplus_{i=1}^{n} i$ denote the cumulative XOR of integers from 1 to $n$, where $\bigoplus$ represents the bitwise XOR operation.