Title: The dynamical system generated by the 3n + 1 function
First published: 1998
Description: The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.
Subjects: Convergence, Sequences (Mathematics), Combinatorial probabilities, Markov processes, Number theory, Mathematics, Information theory, Theory of Computation
LC classification: QA3 .L28 no. 1681, QA292 .L28 no. 1681