I voted to close this question about a "5n+1" version of the Collatz conjecture because it appears to be entirely unmotivated, with no heuristics and not even any substantial numerical evidence.

I don't see the difference in principle between this question and "How many solutions are there to this diophantine equation I've just randomly typed?".

On the other hand, I can imagine this question generating some interesting answers (e.g. applying ideas from Conway's argument that Collatz-like problems are in general undecideable). So I'm opening this thread in case others want to comment.

  • $\begingroup$ I have checked this conjecture by a heuristic applying a mathematuica program and it works. I will pdate the question with the mathematica program so you can test the heuristic by yourself. $\endgroup$ – al-Hwarizmi Aug 10 '13 at 15:20
  • $\begingroup$ Abstarctly I agree. However there are many such questions, some of them even very well received. And, this variant is likely not true (neither is it original), and so I decide it would be simplest to give this as answer. (Also it is weekend and I felt slightly bored.) $\endgroup$ – user9072 Aug 10 '13 at 15:47
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    $\begingroup$ The OP's attempt to pass off a few lines of Mathematica code as a "heuristic" now convinces me that the question should be closed. $\endgroup$ – Steven Landsburg Aug 10 '13 at 16:09
  • $\begingroup$ And, I better had not answered it as somehow I misread it all the time. Sorry for the noise (to those that might mind)! $\endgroup$ – user9072 Aug 10 '13 at 16:33
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    $\begingroup$ Steven we run here with my colleagues through the code tests from $1$ up to one million integers as starting points. The conjecture still holds. quid's response is excellent and supports the heuristic that even a test up to $1000$ would be strong enough. Thanks for your support. $\endgroup$ – al-Hwarizmi Aug 10 '13 at 17:24
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    $\begingroup$ al-Hwarizmi: I do not think that the word "heuristic" means what you think it means. $\endgroup$ – Steven Landsburg Aug 10 '13 at 17:34
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    $\begingroup$ As I said I can see and (abstractly) agree this question might be off-topic, however it is not clear to me what should make it so different than say mathoverflow.net/questions/120511/… for one of many example (which is at +15 no downvote and a massively upvoted answer). $\endgroup$ – user9072 Aug 10 '13 at 19:55
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    $\begingroup$ @quid: Ugh ... . I'd say it's not so different, but I really don't see why there are THAT many upvotes on such question and an answer which probably almost everyone of us could have given. $\endgroup$ – Stefan Kohl Aug 10 '13 at 20:03
  • $\begingroup$ @Stefan Kohl thanks for your comment. $\endgroup$ – al-Hwarizmi Aug 11 '13 at 8:06
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    $\begingroup$ Voting on MO is so weird sometimes... $\endgroup$ – Todd Trimble Aug 11 '13 at 18:23
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    $\begingroup$ @ToddTrimble Less so if you observe voting out in the "real world" (sad to say) $\endgroup$ – Yemon Choi Aug 12 '13 at 4:52

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