Having resisted temptation, I have succumbed to the sirens’ song of “Come on in. The water is fine.”. The following reflects my in… and out for now approach. In the following: If n is odd, then the result of a 3n+1 is even and the formula is rewritten as 3n+12\frac{{3}{n}+{1}}{{2}} If n is even, then n2\frac{{n}}{{2}} is rewritten as 1n+02\frac{{1}{n}+{0}}{{2}} Thus, in my framework 3n+12\frac{{3}{n}+{1}}{{2}} and 1n+02\frac{{1}{n}+{0}}{{2}} are representative of the Collatz Conjecture. Note: In the following table, sequences are extended and linear simplification is performed via y=mx+b Note: The angle of the lines being θ=tan−1mθ={{tan}}^{-{1}}{{m}} establishes their convergence...
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