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内容説明
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.
Book 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.