Conjecture of Pruthviraj Hajari
Conjecture of Pruthviraj Hajari
The iterates x, t(x), t(t(x)),... of the mapping
\[
t(x)=\left\{\begin{array}{cl}
5x+1 & \mbox{ if $x$ is odd,}\\
\left\lceil x/4\right\rceil & \mbox{ if $x$ is even,}
\end{array}
\right.
\]
where \(\lceil\quad\rceil\) denotes the ceiling function ( equivalently
\[
t(x)=\left\{\begin{array}{cl}
5x+1 & \mbox{ if $x$ is odd,}\\
x/4 & \mbox{ if $x\equiv0\pmod{4}$,}\\
(x+2)/4 & \mbox{ if $x\equiv2\pmod{4}$)}
\end{array}
\right.
\]
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.
Last modified 11th December 2020
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