### The Collatz Conjecture

The iterates y, T(y), T(T(y)),... of the 3x+1 function

are printed and the number of steps taken to reach one of the integers
1, 0, -1, -5, -17 is recorded.
It is conjectured that every trajectory starting from a non-zero integer will end in one of the (non-zero) numbers in this list and subsequently cycle:

1,2,1;

-1,-1;

-5,-7,-10,-5;

-17,-25,-37,-55,-82,-41,-61,-91,-136,-68,-34,-17.

Also see Generalized 3x+1 functions and Markov matrices.

*Last modified 2nd February 2006*

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