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- W4300884361 abstract "Much work has been done attempting to understand the dynamic behaviour of the so-called 3x+1 function. It is known that finite sequences of iterations with a given length and a given number of odd terms have some combinatorial properties modulo powers of two. In this paper, we formulate a new hypothesis asserting that the first terms of those sequences have a lower bound which depends on the binary entropy of the ones-ratio. It is in agreement with all computations so far. Furthermore it implies accurate upper bounds for the total stopping time and the maximum excursion of an integer. Theses results are consistent with two previous stochastic models of the 3x+1 problem." @default.
- W4300884361 created "2022-10-04" @default.
- W4300884361 creator A5090478768 @default.
- W4300884361 date "2015-10-06" @default.
- W4300884361 modified "2023-09-27" @default.
- W4300884361 title "The 3x+1 problem: a lower bound hypothesis" @default.
- W4300884361 doi "https://doi.org/10.48550/arxiv.1510.01610" @default.
- W4300884361 hasPublicationYear "2015" @default.
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