On the Equality of ‘Stopping Times’ of Hailstone Numbers

Aditya Dalal

doi:10.20944/preprints202312.1215.v1

Preprint Technical Note Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 December 2023 / Approved: 17 December 2023 / Online: 18 December 2023 (07:18:11 CET)

This short technical note proves some observed novel corollaries of the Collatz Conjecture. For this, a unique ‘Collatz Representation’ of Hailstone numbers has been employed. After that, an extension of this corollary is explained using the fact that only certain differences in the last digit of the ‘Collatz Representation’ gives a whole number difference between numbers. A more general result is obtained. The final proof is for a corollary that some numbers the same number of steps to reach 1 if the Collatz Conjecture is true and all variables are whole numbers.

Collatz Conjecture, Proof, Induction

Computer Science and Mathematics, Algebra and Number Theory

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On the Equality of ‘Stopping Times’ of Hailstone Numbers

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