Number Theory

    

Some New Collatz-like Sequences: If Odd Add d, if Even Divide by 2

Authors: Julian Beauchamp

In this paper, we describe what seems to be a new Collatz-like ("if odd/if even") function, and propose some related conjectures. For any arbitrary positive number, x, iterative operations can be made such that, when even, x is divided by two, and when odd, it is added to odd integer, d. It appears that when x = 1, after sufficient iterations, the sequence always reaches 1, creating a loop. The iterative function can be stated as follows: f(x) = x/2 if x is even, x+d if x is odd.

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[v1] 2026-05-12 21:02:27

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