The aim of this study was to investigate why Collatz series, starting with positive whole numbers, always seem to converge (i.e. end in the 4,2,1 cycle), regardless of their initial behaviour. The results presented here appear to show that symmetrical, Gaussian-like distributions may be inherently involved in the generation of these sequences. The Collatz process appears to draw at random (although not proven or tested in this preliminary report) from this distribution, presumably resulting in its convergent behaviour. It is noted that this is not an attempt or claim to prove or disprove the Collatz conjecture, but only a collection of the results obtained in the aforementioned investigation
Abstract: I propose a numerical table that demonstrates visually that the sequences formed with Co...
Knowledge about algorithms, integers, number theory and recursionThe Collatz conjecture states that ...
In this research an optimal algorithm of the Collatz conjecture is proposed, and the convergence of ...
The aim of this study was to investigate why Collatz series, starting with positive whole numbers, a...
<p>The aim of this study was to investigate why Collatz series, starting with positive whole numbers...
Take any positive integer N. If it is odd, multiply it by three and add one. If it is even, divide i...
This study provides detailed exposition of Collatz 3X + 1 problem which concerns the behavior of the...
The Collatz conjecture, also known as the 3x + 1 conjecture, can be stated in terms of the reduced C...
This document is divided in two parts: first in English and second in French. The document totals 31...
In this paper, we investigate the possible scenarios in which a number does not satisfy the Collatz ...
AbstractThe Collatz conjecture, also known as the 3x+1 conjecture, can be stated in terms of the red...
The Collatz function is defined on the set of positive integers such that for any integer N if N is ...
In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction metho...
The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers for whic...
Collatz dynamic systems present a statistical space that can be studied rigorously. In a previous st...
Abstract: I propose a numerical table that demonstrates visually that the sequences formed with Co...
Knowledge about algorithms, integers, number theory and recursionThe Collatz conjecture states that ...
In this research an optimal algorithm of the Collatz conjecture is proposed, and the convergence of ...
The aim of this study was to investigate why Collatz series, starting with positive whole numbers, a...
<p>The aim of this study was to investigate why Collatz series, starting with positive whole numbers...
Take any positive integer N. If it is odd, multiply it by three and add one. If it is even, divide i...
This study provides detailed exposition of Collatz 3X + 1 problem which concerns the behavior of the...
The Collatz conjecture, also known as the 3x + 1 conjecture, can be stated in terms of the reduced C...
This document is divided in two parts: first in English and second in French. The document totals 31...
In this paper, we investigate the possible scenarios in which a number does not satisfy the Collatz ...
AbstractThe Collatz conjecture, also known as the 3x+1 conjecture, can be stated in terms of the red...
The Collatz function is defined on the set of positive integers such that for any integer N if N is ...
In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction metho...
The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers for whic...
Collatz dynamic systems present a statistical space that can be studied rigorously. In a previous st...
Abstract: I propose a numerical table that demonstrates visually that the sequences formed with Co...
Knowledge about algorithms, integers, number theory and recursionThe Collatz conjecture states that ...
In this research an optimal algorithm of the Collatz conjecture is proposed, and the convergence of ...