Novel Theorems and Algorithms Relating to the Collatz Conjecture

Schwob, Michael R.; Shiue, Peter Jau-Shyong; Venkat, Rama

doi:10.1155/2021/5754439

Cited by 7 publications

(2 citation statements)

References 15 publications

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“…• Schwob et al [10] proposed several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture.…”

Section: Introductionmentioning

confidence: 99%

A Conjecture from Collatz Conjecture: Elevation by Folding

Al‐Rawajfeh¹

2023

GLM

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The Collatz Conjecture proposed in 1937 by German mathematician Lothar Collatz remains unsolved. It states that: let ℕ be the set of all positive integers and n ϵ ℕ, then: any positive integer n will collapse to 1 by applying the rules of the conjecture: 3n+1 (for odd numbers) and n/2 (for even numbers). In this work, a new conjecture was stated from Collatz conjecture. Percentage crystallinity was defined and a unique solution of the elevation (reverse) of the cyclone part and the whole stem was suggested. The % Crystallinity of the 512-line on the stem is 100% while it is 68% for the 184-line. The only number, f(n) = 112n, resulting from multiplication of prime numbers, that satisfies the elevation of Collatz cyclone is 112 (i.e., n = 1), and for the elevation of the stem, the multiplications of 112 are valid (i.e., n = 2, 4, 8, 16, …). When 112 is folded, it gives the following pairs: 56, 28, 14, and 7, which correspond the 7 th , 6 th , 5 th , 4 th , and 3 rd dimensions, respectively. This elevation conjecture will lead to many applications, for example, the 9 th planet can be suggested to be devoured in a black Hole that may be resulted from the death of the symmetric sun of our solar system's sun.

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Section: Introductionmentioning

confidence: 99%

A Conjecture from Collatz Conjecture: Elevation by Folding

Al‐Rawajfeh¹

2023

GLM

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“…Recently, a preprint claimed to have reached the solution, but the file still is not posted [22]. More recently, a paper [23] indicates the intractable nature of the conjecture.…”

Section: Introductionmentioning

confidence: 99%

Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture

Carbó‐Dorca

Perelman

2022

Journal of Mathematical Sciences and Modelling

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Using simple arguments derived from the Boolean hypercube configuration, the structure of natural spaces, and the recursive exponential generation of the set of natural numbers, a linear classification of the natural numbers is presented. The definition of a pseudolinear Collatz operator, the description of the set of powers of $2$, and the construction of the natural numbers via this power set might heuristically prove the Collatz conjecture from an empirical point of view.

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