Conjecture of Pruthviraj Hajari

The iterates x, t(x), t(t(x)),... of the mapping

t(x) = 8x if x is odd
t(x) = ⌊ x/3 if x is even,
where ⌊  ⌋  denotes the floor function.

Equivalently

t(x) = 8x if x is odd
t(x) = x/3 if x ≡ 0 (mod 6)
t(x) = (x - 2)/3 if x ≡ 2 (mod 6)
t(x) = (x - 1)/3 if x ≡ 4 (mod 6)

are conjectured by Pruthviraj Hajari to eventually reach 0 if x ≥ 0. (See MathOverflow question.)

It seems certain that if x < 0, then tn(x) will eventually reach one of the cycles -3 → -24 → -8 → -3, or -5 → -40 → -14 → -5.

Enter x :

Last modified 10th December 2020
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