From the succession of Collatz Personalized, the veracity of the same can be deduced
Year: 2025
Type: article
Abstract: One of the problems of elementary mathematics, still unsolved, is the Collatz conjecture (after the mathematician Lothar Collatz). It concerns the following function between natural numbers: f: N→ N with f(N)= N/2 if N is even or f(N)=(3*N+1) if N is odd.By iterating the function several times, after a certain number of iterations we get the number 1 and continuing the iterations we have the cycle 1 → 4 → 2 → 1. Then the initial number N, in subsequent iterations, is multiplied by 3 (adding 1) and divided by 2, so that we have a succession of odd steps (when multiplying by 3 and adding 1) and even passes (when dividing by 2) that, after a certain total number of even passes bi and a certain total number of odd steps to, converges to 1.In my 2 previous papers, a custom sequence of the Collatz function has been defined, formulated on a modular basis and oriented to reduce the number of iterations required for convergence. Thanks to algorithmic coding and a diagrammatic structure, the method allows for simplified tracking of odd and even steps, with obvious computational advantages.In this work I also verify Theorem No. 6.2 of reference [1] and prove the same using the Theorem of the intersection of two lines in paragraph 5.
Author: ARDITO, NICOLA
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7084601996
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