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On the intimate association between even binary palindromic words and the Collatz-Hailstone iterations

Authors

Theophanes Raptis Information Physics Institute, Athens, Greece

DOI:

Keywords:

Collatz conjecture, Hailstone sequences, Binary palindromes, Iterative dynamics

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,...,2^2k-1]. A set of equivalent reformulations of the problem are also presented.

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Published

2024-10-08

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2024-10-15 (2)
2024-10-08 (1)

How to Cite

Raptis, T. (2024). On the intimate association between even binary palindromic words and the Collatz-Hailstone iterations. IPI Letters, 2(3), 1–39. https://doi.org/10.59973/ipil.130