منابع مشابه
More Jabber about the Collatz Conjecture and a Closed Form for Detecting Cycles on Special Subsequences [Assertion: Collatz cycles]
In [ref 1] apparently published in 2006 professor Cadogan presents an interesting function that maps natural numbers into a two dimensional array based on how many ones the number trails off with. The length of trailing one's is said to be the row index. The rest of the number, divided by 2, is the column index. He then shows that applying the Collatz function reduces the ending string of ones ...
متن کاملOptimal Bounds for the Length of Rational Collatz Cycles
We consider the arithmetics of Collatz cycles in Q(2)]. In particular , we prove optimal estimates for the length of a cycle in terms of its minimum. As an application, we derive an improved version of Eliahou's criterion , and we show that the length of (integer) Collatz cycles which do not contain 1, is at least 102 225 496 provided the Collatz conjecture is veriied for all initial values x 0...
متن کاملCollatz Conjecture
My math 301 Term paper will be concerned with exploring the Collatz conjecture. I will discuss the importance and interest of this conjecture; what progress has been made on this problem and who made it. I will also explore whether any connections have been made between the Collatz conjecture and other mathematical problems.
متن کاملω-rewriting the Collatz problem
The Collatz problem is comprised of two distinct, separate questions: existence of eventually periodic Collatz reductions with a nontrivial period, and existence of period-free Collatz reductions. This paper introduces a few distinct, related formalizations of the Collatz dynamics as term rewriting systems, using elementary concepts from the theory of state transition dynamics. Some of the subj...
متن کاملThe Undecidability of the Generalized Collatz Problem
The Collatz problem, widely known as the 3x + 1 problem, asks whether or not a certain simple iterative process halts on all inputs. We build on earlier work by J. H. Conway, and show that a natural generalization of the Collatz problem is recursively undecidable.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2008
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa134-3-1