Density Bounds for the 3x + 1 Problem. I. Tree-Search Method
نویسندگان
چکیده
منابع مشابه
Method Study on the 3x+1 Problem
The 3x+1 problem is one of the most classical problems in computer science, related to many fields. As it is thought by scientists a highly hard problem, resolving it successfully not only can improve the research in many relating fields, but also be meaningful to the method study. By deep analyzing the 3x+1 calculation process with the input positive integer becoming greater, we find a useful ...
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15 صفحه اولA Solution to the 3x + 1 Problem
We present several proofs of the 3x + 1 Conjecture, which asserts that repeated iterations of the function C(x) = (3x + 1)/(2a) always terminate in 1 Here x is an odd, positive integer, and a is the largest positive integer such that the denominator divides the numerator. Our first proofs are based on a structure called “tuple-sets” that represents the 3x + 1 function in the “forward” (as oppos...
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The 3x + 1 function T(x) takes the values (3x+l)/2 if x is odd and x/2 if x is even. Let a be any integer with a £ 0 (mod 3). If na(x) counts the number of n with |«| < x which eventually reach a under iteration by T, then for all sufficiently large x , na(x) > xsx . The proof is based on solving nonlinear programming problems constructed using difference inequalities of Krasikov.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1995
ISSN: 0025-5718
DOI: 10.2307/2153345