Timeline for Question on consecutive integers with similar prime factorizations
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2022 at 22:26 | answer | added | Andrew Granville | timeline score: 1 | |
| Jun 24, 2022 at 21:01 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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| Jan 15, 2013 at 20:19 | vote | accept | David Corwin | ||
| Nov 16, 2012 at 5:45 | vote | accept | David Corwin | ||
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| Nov 10, 2012 at 15:05 | answer | added | Anonymous | timeline score: 16 | |
| Nov 10, 2012 at 2:18 | history | edited | Eric Naslund |
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| Nov 9, 2012 at 18:06 | answer | added | Eric Naslund | timeline score: 5 | |
| Nov 9, 2012 at 16:32 | history | edited | David Corwin | CC BY-SA 3.0 |
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| Aug 11, 2010 at 9:20 | answer | added | Aaron Meyerowitz | timeline score: 9 | |
| Jul 23, 2010 at 10:46 | comment | added | Wadim Zudilin | I would say that Ken Fan's restricted version of your question "Are there infinitely many integers $n$ such that $n$ is factorially equivalent to $n+1$?" was more successful. It seems that nobody mentioned here a very elegant answer in the affirmative: mathoverflow.net/questions/33037/…. | |
| Jul 21, 2010 at 6:23 | answer | added | Tom Sirgedas | timeline score: 5 | |
| Jul 20, 2010 at 21:56 | answer | added | Andreas Rüdinger | timeline score: 3 | |
| Jul 20, 2010 at 17:17 | answer | added | Ken Fan | timeline score: 9 | |
| Jul 19, 2010 at 13:30 | comment | added | Charles | @Charles Matthews: I think that heuristic suggests only finitely many pairs. But of course we believe that there are infinitely many (e.g., twin prime conjecture), so I think you're right to be suspicious about ignoring small primes and the like. | |
| Jul 19, 2010 at 13:22 | comment | added | Charles | @Will Jagy: Sloane's A052214 has triples. These are actually pretty dense for small values: the 10,000-th is only 1188861. Quadruples seem much sparser. oeis.org/classic/A052214 | |
| Jul 19, 2010 at 10:04 | comment | added | Charles Matthews | Yes, parity seems to give something here. The other effect worth thinking through is the number of signatures, given that the possible signatures for integers of size N is apparently the partition function summed up to log N. We certainly know the average order of the partition function. So (this currently looks a bit crude, since small primes are not dealt with) what do we expect from random adjacencies of the same partition? | |
| Jul 19, 2010 at 7:30 | comment | added | Charles Matthews | Can you conclude much from small numbers? The product of the first four primes is 210. Below that you have only a handful of signatures, and some adjacencies are to be expected. | |
| Jul 19, 2010 at 7:18 | history | edited | Charles Matthews | CC BY-SA 2.5 |
downcase
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| Jul 19, 2010 at 0:29 | comment | added | Will Jagy | You have a triple, (33, 34, 35). It seems you could cut down considerably on frequency by considering triples or quadruples. Is it known there are infinitely many triples with $$ d(n) = d(n+1) = d(n+2) $$ or that there are not infinitely many? | |
| Jul 19, 2010 at 0:07 | history | edited | David Corwin | CC BY-SA 2.5 |
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| Jul 18, 2010 at 22:24 | comment | added | Charles | I can't answer your question, but note that your sequence is Sloane's A052213. [1] oeis.org/classic/A052213 | |
| Jul 18, 2010 at 21:57 | history | asked | David Corwin | CC BY-SA 2.5 |