This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.
In this paper we have used the mathematical induction to demonstrate a property of the huts related to the convergence of the syracuse sequences towards the trivial cycle. Let's explain it. First we multiply the terms of the syracuse orbits by 3 and we group these terms into equivalence classes following this relation: l ~l' if k<l<m and k'<l'<m' ,v_2(k)=v_2(k') and v_2(m)=v_2(m') k,k',m,m' multiples of 6 such that m=k+6 and m'=k'+6,l and l' odd multiples of 3 . It is this equivalence class that we call 'hut'. After that we order this set and we apply mathematical induction on a property of its elements related to the convergence of the sequences towards the trivial cycle 4 2 1. For more technical informations,the reader is invited to read the paper,and to temporarily abandon its skepticism .
