Conjecture of Pruthviraj Hajari

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

t(x) = 5x + 1 if x is odd
t(x) = x/4 if x is even,
where ⌈  ⌉  denotes the ceiling function.

Equivalently

t(x) = 5x+ 1 if x is odd
t(x) = x/4 if x ≡ 0 (mod 4)
t(x) = (x + 2)/4 if x ≡ 2 (mod 4)

are conjectured by Pruthviraj Hajari to eventually reach 1 if x > 0. (See MathOverflow question.)

It seems certain that if x ≠ 0, then tn(x) will eventually reach one of the cycles 0 → 0, -1 → -4 → -1, or 1 → 6 → 2 → 1, or -3 → -14 → -3.

Enter x :

Last modified 11th December 2020
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