A note on the 3x+1 conjecture

2021/10/23 by J. Llibre, Clàudìa Valls, Llibre, J. +1
Mathematics · #11A99 #37P99 #Benford’s Law and Fraud Detection #FOS: Mathematics #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.2110.12228

openalex publication_date 2021/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let g be a map from the set of positive integers into itself defined as follows: Let x be a positive integer. If x is odd, then g(x)=3x+1, and if x is even, then g(x)=x/2. The 3x+1 conjecture, also called the Collatz conjecture, states: For any positive integer x there exists another positive integer m such that the m-iterate of x under the map g is equal to 1, i.e. g^m(x)=1. We provide some information related with this conjecture.

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