Lu Pei's Collatz type conjecture

The iterates y, t(y), t(t(y)),... of Lu Pei's mapping

t(x) = x/3 if x ≡ 0 (mod 3)
t(x) = (4x-1)/3 if x ≡ 1 (mod 3)
t(x) = (4x+1)/3 if x ≡ -1 (mod 3)

are printed and the number of steps taken to reach one of the integers 1 or -1 starting from a positive or negative integer is recorded.

This remarkable phenomenon was discovered by Lu Pei and communicated to Keith Matthews in November 1997.

We remark that the iterates of -x are the negative of the iterates of x, so it is enough to consider positive starting values x.

Also see a generalization to d branches.

Enter x (≠ 0):

Last modified 10th January 2011
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