This question is kind of related to programming but my question only relates to math in a theoretical sense. I was trying to implement a Collatz conjecture algorithm that calculates the steps it needs for a number to reach $1$.
function:
if x = 1 return;
else
steps = steps + 1
if x is pair:
function(x/2)
if x is odd:
function(3x+1)
Accidentally I wrote in the last line, $3x-1$, which caused an infinite loop where the number after a few recursions becomes it self again. I just want to know what this accidental "conjecture" so to speak is, as to give a name to my bug.
This is actually an extension of the Collatz problem to negative inputs, so I would call it that. To see this, exchange $x$ for $-x$ in your calculation. Thus with your typo, $5$ gives
$5,14,7,20,10,5,$
whereas the true Collatz recursion with the input negative yields
$-5,-14,-7,-20,-10,-5.$
As can be seen here, this negative extension of the Collatz problem has multiple cycles; it does not automatically reach $(-)1$.