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140122 ||| eng |
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|a 9783540696773
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| 100 |
1 |
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|a Wirsching, Günther J.
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| 245 |
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|a The Dynamical System Generated by the 3n+1 Function
|h Elektronische Ressource
|c by Günther J. Wirsching
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| 250 |
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|a 1st ed. 1998
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1998, 1998
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| 300 |
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|a VIII, 164 p
|b online resource
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| 505 |
0 |
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|a Some ideas around 3n+1 iterations -- Analysis of the Collatz graph -- 3-adic averages of counting functions -- An asymptotically homogeneous Markov chain -- Mixing and predecessor density
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| 653 |
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|a Number theory
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| 653 |
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|a Computer science
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| 653 |
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|a Number Theory
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| 653 |
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|a Theory of Computation
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Lecture Notes in Mathematics
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| 028 |
5 |
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|a 10.1007/BFb0095985
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| 856 |
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|u https://doi.org/10.1007/BFb0095985?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 512.7
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| 520 |
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|a 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
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