Results 51 to 60 of about 509 (137)
On the nonexistence of cycles for the Collatz function
, 2012 This paper has been withdrawn by the author because (k+1 ...
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General formulas of global characteristic coefficients of Collatz function
, 2021 The purpose of this paper is to show three general formulas of three global characteristic coefficients of Collatz function. The Collatz function is defined by the following operation on an arbitrary positive integer if N is odd multiply it by 3 and add 1 then the sum obtained is divided by 2, if N is even divide it by 2.
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Resolution of Generalized Collatz Functions
The Collatz Conjecture and its generalized class of parity-driven recurrence relations areshown to obey recursive compression symmetries governed by parity, modular class, and log-arithmic descent. In this paper, we extend the proof structure established for the classical3n + 1 problem to the full family of parity-based functions, demonstrating that ...
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Compressed Function for Collatz Dynamics
We present a compressed function for the analysis of Collatz dynamics that generalizes the classical accelerated iteration by eliminating intermediate even numbers and reducing trajectory length significantly. This novel formulation condenses multiple steps of the standard iteration into single jumps, producing a reduced sequence that preserves the ...
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Generalized Collatz functions defined on arithmetic progressions of real numbers
, 2021 {"references": ["Raouf Rajab. Les fonctions de Collatz et leurs propri\u00e9t\u00e9s. 2021. \u27e8hal-03328322v2\u27e9"]}
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Structural invariant of Collatz function
Prove me wrong and fine me with an amount of your choice!
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Entomopathogens and Parasitoids Allied in Biocontrol: A Systematic Review. [PDF]
Pathogens, 2023 Koller J +4 more
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Plant families exhibit unique geographic trends in C4 richness and cover in Australia. [PDF]
PLoS One, 2022 Munroe SEM +7 more
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Evaluation of a critical incident management system on mental health in lifeguard organisations: a retrospective study. [PDF]
BMJ Open Sport Exerc Med, 2023 Breindahl N +3 more
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