Following up on my last question, Last Question.
I have also noticed the following:
If $x \bmod 5=0$ : execute $x/5$, or elseIf $x$ ends in $1$ : execute $(x⋅2)+3$, or elseif $x$ ends in $3$ : execute $(x⋅4)+3$ , or elseif $x$ ends in $7$ : execute $(x⋅6)+3$, or elseif $x$ ends in $9$ : execute $(x⋅8)+3$.
This time they all end in either $1$ or $3$ or $27$.
In comparison, I have also tried the following: If $x \bmod 5=0$ : execute $x/5$, or elseIf $x$ ends in $1$ : execute $(x⋅4)+1$, or elseif $x$ ends in $3$ : execute $(x⋅8)+1$ , or elseif $x$ ends in $7$ : execute $(x⋅12)+1$, or elseif $x$ ends in $9$ : execute $(x⋅16)+1$.
In this case I had runs that seem to go infinite.
My question this time is:
Are there any generalized rules as far as when these conjectures work and when they don't ?