Recently, I have been reading about the Collatz Conjecture and on the wikipedia page for it, came across the fact that:
Rigorous bounds
Although it is not known rigorously whether all positive numbers eventually reach one according to the Collatz iteration, it is known that many numbers do so. In particular, Krasikov and Lagarias showed that the number of integers in the interval $[1,x]$ that eventually reach one is at least proportional to $x^{0.84}$.
Would anyone know where I can learn more about this bound (why $0.84$?) or where the paper was published (is it online?). Cheers
The first Google search result for
Krasikov and Lagariasis the relevant article on arXiv.