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- W2949427906 abstract "In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture. We then prove our main result about the iterates of U (which is directly related to both of these conjectures). We also introduce the flipped 3x+1 function widetilde U and prove an analogous result for its trajectories. In the final section, we pose some interesting questions about the iterates of U (and widetilde U), prove a couple of simple results about the iterates of U and widetilde U, introduce other related functions and propose yet more conjectures and questions about their iterates. It's our hope that the results, conjectures and questions presented here will be not only relevant to the 3n+1 conjecture itself, but also of interest in their own right." @default.
- W2949427906 created "2019-06-27" @default.
- W2949427906 creator A5070194226 @default.
- W2949427906 date "2004-10-22" @default.
- W2949427906 modified "2023-09-27" @default.
- W2949427906 title "The Real 3x+1 Problem" @default.
- W2949427906 hasPublicationYear "2004" @default.
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