On Sur Samtani's Accelerated Collatz Function
The result's identifiers
Result code in 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>
Result on the web
<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
—
Alternative languages
Result language
angličtina
Original language name
On Sur Samtani's Accelerated Collatz Function
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
O - Miscellaneous
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů