Contents Next: Introduction. The 3x + 1 Problem and its Generalizations ... Generalizations of problem . Algorithmic decidability questions. Existence of stopping ...

1 Problem , the Syracuse Problem , the Collatz Problem , Ulam's Problem , ... Other equivalent formulations of the 3x + 1 problem are given in the literature; we base our ...

The 3x +1 problem is a special case of a more general class of problems which are equally tantalizing, but about which one can make accurate predictions. ...

The 3x + 1 problem can be stated as follows. For any positive integer n, if n is odd compute ... 1 problem ) and the current research indicates that the conjecture is ...

The 3x + 1 problem concerns the following operation on integers: if ... The 3x + 1 problem concerns what happens if one iterates this operation starting from a given ...

The 3x + 1 conjecture asserts that iteration of this function, starting from any ... He raised the question that W contained all positive integers, a problem ...

3x + 1 Problem . f:=proc(x) if x mod 2 =0 then x/2 else 3*x+1 fi; end; Working under Maple without the spreadsheet ...

Introduction: The Collatz Conjecture, also known as the 3x +1 problem , is simple by definition, but upon further research it becomes a very

Generalizations of the 3x + 1 problem and. connections with Markov matrices and chains ... de?nes a mapping T : Z Z, called a generalized 3x + 1 mapping. ...

The Collatz Conjecture, also known as the 3x +1 problem , is simple by definition, but upon further research it becomes a very complex theory. ...