On the intimate association between even binary palindromic words and the Collatz-Hailstone iterations
Year: 2024
Type: article
Abstract: The celebrated 3x+1 problem is reformulated via the use of an analytic expression of the trailing zeros sequence resulting in a single branch formula f(x)+1 with a unique fixed point. The resultant formula f(x) is also found to coincide with that of the discrete derivative of the sorted sequence of fixed points of the reflection operator on even binary palindromes of fixed even length \textit{2k} in any interval [0,...,22k-1]. A set of equivalent reformulations of the problem are also presented.
Source: IPI Letters
DOI: 10.59973/ipil.130
Author: Theophanes Raptis
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403224448