A 3-branched generalized-Collatz Conjecture

The iterates y, t(y), t(t(y)),... of the function

t(x) = 2x if 3 divides x,
t(x) = (7x+2)/3 if 3 divides x-1,
t(x) = (x-2)/3 if 3 divides x+1,

are printed and the number of steps taken to reach either a multiple of 3, or else one of the cycles -1,-1 or -2,-4,-2 is recorded.

It is conjectured by Keith Matthews (who offers a $100 Australian prize for a resolution of this conjecture) that every trajectory will find its way into the zero residue class (mod 3) or else enter one of three cycles: 0, 0; -1,-1; -2,-4,-2. (See online survey on generalized 3x+1 mappings.)

The algorithm is performed with starting values y= 3M+1 and y=3M-1.

Enter M:

Last modified 12th March 2010
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