The 3x + 1 problem is de?ned by a sequence of natural numbers, generated ... 2. The approach can be applied to the 3x 1 problem , de?ned by T (x) ...

Author(s): Collatz   Subject: Number Theory " Combinatorial N.T.   ... In The 3x +1 Problem : An Annotated Bibliography, II (2001-), Lagarias explains why this ...

Complex dynamics of some generalizations of the 3x +1 function. These images show the complex dynamics of some generalizations of the 3x +1 problem . ...

I have just learned (December 1998) that this problem is older: it is the "original Collatz problem " from the 1930s (before the famous 3x +1 problem ) ...

n:=77671:m:=[ ]:while n>1 do if n mod 2 = 0 then n:=n/2 else n:=3*n+1 ... Reference: Martin Gardner, Wheels, Life and other Mathematical Amusements, p. ...

The NAS-3X is typically deployed unattended for periods of 1 to 3 ... A Solution to the 3x + 1 Problem Charles Cadogan. The 3x + 1 conjecture asserts that in the sequence of ...

The 3x +1 problem concerns the iteration of the function T: N+ ® N+ defined as: ... The 3x +1 Conjecture asserts that repeated iteration of the function T on any ...

1 . Problem : Find f-1(x) of 3x + 1 Solution: The equation is y = 3x + 1 . Interchange x and y. x = 3y + 1 Solve for y. x - 1 = 3y (x - 1 )/3 = y f-1(x) = (x - 1 )/3 ...

The Collatz problem , widely known as the 3x + 1 problem , asks. whether or not a certain ... generalization of the Collatz problem is recursively undecidable. ...

The seven problems who solutions will bring $1 ,000,000 each from the Clay ... problems below (Goldbach's Conjecture, The Kolakoski sequence, The 3x +1 Problem , ...