(12C) 3n + 1 conjecture

[Joe Horn]

(07-07-2018 04:57 PM)Dieter Wrote:  In this case you can omit the PSE completely and wait until the program finishes with a "1".

Which is exactly why I wrote this:

(07-07-2018 02:24 PM)Joe Horn Wrote:  You might be thinking, "...why not just eliminate the PSE entirely..."

(07-07-2018 04:57 PM)Dieter Wrote:  But the fun is watching the numbers go up und down. ;-)

Which is exactly why I wrote this:

(07-07-2018 02:24 PM)Joe Horn Wrote:  "This would still test the hypothesis, and run MUCH faster, but it would be really boring to watch!" To which I would reply, "Quite right."

Of course, my program DOES show the numbers going up and down. It merely skips the unnecessary 3X+1 terms, since EVERY 3X+1 must always be even, so you might as well save time by dividing those by 2 right away, no?

(07-07-2018 04:57 PM)Dieter Wrote:  Regarding the program: it does not display 3x+1 but (3x+1)/2.

But that's PRECISELY what my goal is. I don't want to display those terms, because they are unnecessary to attain all the stated goals of this program! My program does what the OP asked for, AND it shows the numbers going up and down (like hailstones in a storm), AND it's shorter and faster.

(07-07-2018 04:57 PM)Dieter Wrote:  If you modify your program accordingly ... it will return the correct sequence.

"Correct sequence"? The Wikipedia page about the Collatz Conjecture says, "The standard Collatz map defined above is optimized by replacing the relation 3n+1 with the common substitute 'shortcut' relation (3n+1)/2." That's "correct" enough for me.

Disclaimer: The above is near and dear to my heart because it was the subject of my HHC 2014 talk, "Hailstone Numbers: A Pattern Has Been Found", in which the above "shortcut" was called the "Modified Syracuse Algorithm" which can be used to test the original Collatz Conjecture more efficiently than using the original 3x+1 "Syracuse Algorithm".