On Sur Samtani's Accelerated Collatz Function
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10510681" target="_blank" >RIV/00216208:11320/25:10510681 - isvavai.cz</a>
Výsledek na webu
<a href="https://drive.google.com/file/d/1foWFe2PQnm8LgDN0Y1bEiLICVo3VLKNQ/view" target="_blank" >https://drive.google.com/file/d/1foWFe2PQnm8LgDN0Y1bEiLICVo3VLKNQ/view</a>
DOI - Digital Object Identifier
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Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On Sur Samtani's Accelerated Collatz Function
Popis výsledku v původním jazyce
The Collatz conjecture, a longstanding unsolved problem in mathematics,centers around the Collatz function that maps the set of positive integers intoitself. The conjecture states that, for each positive integer n, the least memberin the trajectory generated by iterating the Collatz function from n is 1. Overthe years, this conjecture has sparked numerous formulations and reformulations,each shedding light on different facets of the problem. Outstandingamong these formulations is the Syracuse function operating similarly to theCollatz function but on the odd positive integers only. Recently, Sur Samtani,introduced an accelerated version of the Collatz function that can streamlineanalysis and potentially pinpoint counterexamples candidates.In this short note, building on Sur Samtani's observation concerning representationof odd positive integers and behavior of Sur Samtani's function,we present and study two acceleration functions. One accelerates Sur Samtani'sfunction and one accelerates the Syracuse function. The former hashelped to further reduce the set of potential counterexamples of nontrivialcyclic trajectories presented by Sur Samtani. For comparison, relative ratesof accelerations are illustrated on a number of examples.
Název v anglickém jazyce
On Sur Samtani's Accelerated Collatz Function
Popis výsledku anglicky
The Collatz conjecture, a longstanding unsolved problem in mathematics,centers around the Collatz function that maps the set of positive integers intoitself. The conjecture states that, for each positive integer n, the least memberin the trajectory generated by iterating the Collatz function from n is 1. Overthe years, this conjecture has sparked numerous formulations and reformulations,each shedding light on different facets of the problem. Outstandingamong these formulations is the Syracuse function operating similarly to theCollatz function but on the odd positive integers only. Recently, Sur Samtani,introduced an accelerated version of the Collatz function that can streamlineanalysis and potentially pinpoint counterexamples candidates.In this short note, building on Sur Samtani's observation concerning representationof odd positive integers and behavior of Sur Samtani's function,we present and study two acceleration functions. One accelerates Sur Samtani'sfunction and one accelerates the Syracuse function. The former hashelped to further reduce the set of potential counterexamples of nontrivialcyclic trajectories presented by Sur Samtani. For comparison, relative ratesof accelerations are illustrated on a number of examples.
Klasifikace
Druh
O - Ostatní výsledky
CEP obor
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OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
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Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů