A new thermodynamic limit for the [(3•n-1)/2, n/2)] Collatz sequence

Abstract

We consider a new way to analyse the cardinality of the odd and of the even numbers emerging in the above Collatz sequence and we find that as the chalice of the inverse orbits grows to infinity the cardinality of them are the same, i.e. we have a limit which is different from the usual one with a vertical depth.