$3n+1$ problem: an heuristic lower bound for the number of integers connected to 1 and less than $x$

Abstract

This paper gives an heuristic lower bound for the number of integers connected to 1 and less than $x$, $\theta (x)>0.9x,$ in the context of the $3n+1$ problem.

References in corpus (4)

• The 3x+1 Problem and Integer Representations
• Some identities involving polynomial coefficients
• A Note on Extended Binomial Coefficients
• A simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem