Timeline for Not especially famous, long-open problems which anyone can understand
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2022 at 11:33 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
replaced the dead link
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| Aug 19, 2012 at 18:40 | comment | added | Marc Chamberland | Question #2 was addressed in the paper math.grinnell.edu/~chamberl/papers/mario_digits.pdf The real problem concerns the initial value $x_0=2$. It can be shown that the set of initial values which produce an unbounded sequence $\{x_n\}$ has full measure, so from a probabilistic perspective, one expects the statement in question 2 to hold. | |
| Jul 27, 2012 at 21:15 | comment | added | Owen Biesel | @Davidac897: I think the conjecture part of #3 is the first sentence: "The largest integer... is 462." If I'm reading the rest correctly, it's known that if the conjecture is false, it's only because of a single counterexample that must be greater than 200 billion. | |
| Jul 22, 2012 at 20:24 | comment | added | David Corwin | For #3, you say that 462 is the largest integer with this property, yet that there exists at most one such integer $n<462$. Do you mean to say that 462 is the largest integer with this property other than one possibly $n>462$? | |
| Jun 23, 2012 at 19:17 | comment | added | David Feldman | I'm wondering if I "get" #2. I see an implicit map from $S^1$ to $S^1$ of index 2, so yes, it seems generally hard to understand the dynamical fate of a given starting value. A similar question might ask if the binary expansion of $\sqrt{2}$ contains strings of 0's of arbitrary length. But is #2 specifically conjugate to something more familiar? | |
| Jun 23, 2012 at 0:47 | comment | added | Noam D. Elkies | Yes, I understand why it's difficult... And it seems that the third one that you added since then is another incarnation of the "numeri idonei" problem. | |
| Jun 22, 2012 at 22:53 | history | edited | Richard Stanley | CC BY-SA 3.0 |
Item #3 added.
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| Jun 22, 2012 at 20:31 | comment | added | Richard Stanley | @Noam: I can't recall. Someone mentioned this to me many years ago. A little thought will show why this is so difficult. | |
| Jun 22, 2012 at 20:28 | history | edited | Richard Stanley | CC BY-SA 3.0 |
$n\geq 1$ replaced with $n\geq 0$
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| Jun 22, 2012 at 20:24 | comment | added | Noam D. Elkies | Where does the second of these come from? | |
| Jun 22, 2012 at 20:20 | history | answered | Richard Stanley | CC BY-SA 3.0 |