рекурентна послідовність

ON THE MATHEMATICAL MODEL OF THE TRANSFORMATION OF NATURAL NUMBERS BY A FUNCTION OF A SPLIT TYPE

In this work justified incorrectness of the algorithm proposed in the publication "M. Remer.[A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture. Journal of Applied Mathematics and Physics. Vol.11 No.8, August 2023"] in terms of the Collatz conjecture. And also that the transformation -3(-n) - 1 is not equivalent to Collatz's conjecture on the natural numbers 3n + 1. The obtained results can be used in further studies of the Collatz hypothesis

Methods of Correcting Errors in Messages Encoded by Fibonacci Matrices

The main problems of detection and available methods of correcting errors in encoded messages with Fibonacci matrices, which make it possible to find and correct one, two and three errors in the same or different lines of the code word, are analyzed. It has been found that even in the last decade, many scientists have published a significant number of various publications, each of which to one degree or another substantiates the expediency of using Fibonacci matrices for (de)coding data.

FROM NEWTON'S BINOMIAL AND PASCAL’S TRIANGLE TO СOLLATZ'S PROBLEM

It is shown that: 1. The sequence {20,21, 22, 23, 24, 25, 26, 27,28,...} that forms the main graph m=1 of Collatz is related to the power transformation of Newton's binomial (1+1)ξ, ξ=0, 1, 2, 3,... 2. The main Kmain and side m >1 graphs and their corresponding sequences {Kmain } and {Km } are related by the relation {Km }=m⋅{Kmain }. 3.