# Publication [4.8] of Tomás Oliveira e Silva

Instead, bookmark its parent page (http://sweet.ua.pt/tos/bib.html).

## Reference

**Tomás Oliveira e Silva**, "Maximum Excursion and Stopping Time Record-Holders for the *3x+1* Problem: Computational Results," *Mathematics of Computation*, vol. 68, no. 225, pp. 371-384, Jan. 1999. Up to date computational results can be found at http://sweet.ua.pt/tos/3x+1.html or at http://sweet.ua.pt/tos/3x_plus_1.html.

## Abstract

This paper presents some results concerning the search for initial values to the so-called *3x+1* problem which give rise either to function iterates that attain a maximum value higher than all function iterates for all smaller initial values, or which have a stopping time higher than those of all smaller initial values.
Our computational results suggest that for an initial value of *n*, the maximum value of the function iterates is bounded from above by *n^2f(n)*, with *f(n)* either a constant or a very slowly increasing function of *n*.
As a by-product of this (exhaustive) search, which was performed up to *n=3·2^53>2.702·10^16*, the *3x+1* conjecture was verified up to that same number.

## BibTeX entry

@Article { Oliveira.e.Silva-1999-1-MESTRH, author = {Oliveira e Silva, Tom{\'a}s}, title = {Maximum Excursion and Stopping Time Record-Holders for the $3x+1$ Problem: Computational Results}, journal = {Mathematics of Computation}, year = {1999}, volume = {68}, number = {225}, pages = {371--384}, month = Jan, note = {Up to date computational results can be found at \url{http://sweet.ua.pt/tos/3x+1.html} or at \url{http://sweet.ua.pt/tos/3x_plus_1.html}.} }