The ultimate challenge : the 3x+1 problem
Brings together a collection of articles written about the topic over the last forty years. The articles approach the material from different directions and using different flavours of mathematics, all the while trying to solve the problem.
Print Book, English, ©2010
American Mathematical Society, Providence, R.I., ©2010
xiv, 344 p. : il. ; 27 cm
9780821849408, 0821849409
1025667820
Part I. Overview and introductionThe 3𝑥+1 problem: An overviewThe 3𝑥+1 problem and its generalizationsPart II. Survey papersA 3𝑥+1 Survey: Number theory and dynamical systemsGeneralized 3𝑥+1 mappings: Markov chains and ergodic theoryGeneralized 3𝑥+1 functions and the theory of computationPart III. Stochastic modelling and computation papersStochastic models for the 3𝑥+1 and 5𝑥+1 problems and related problemsEmpirical verification of the 3𝑥+1 and related conjecturesPart IV. Reprinted early papersCyclic sequences and Frieze patterns (The Fourth Felix Behrend Memorial Lecture)Unpredictable iterationsIteration of the number-theoretic function 𝑓(2𝑛)=𝑛,𝑓(2𝑛+1)=3𝑛+2Don’t try to solve these problems!On the motivation and origin of the (3𝑛+1)-problemFRACTRAN: A simple universal programming language for arithmeticPart V. Annotated bibliographyThe 3𝑥+1 problem: An annotated bibliography (1963–1999)