The Dynamical System Generated by the 3n+1 Function

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 focu...

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Bibliographic Details
Main Author: Wirsching, Günther J
Format: Book
Language:English
Subjects:
Combinatorial probabilities
Convergence
Information theory
Mathematics
Mathematics and Statistics
Number Theory
Sequences (Mathematics)
Theory of Computation
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Summary: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.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0095985