Timeline for Does $a_{i}(n)$ hit every positive integers infinitely many times for all $i\ge1$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2021 at 20:33 | comment | added | Alkan | Thanks for your comment and suggestion, I agree in general. | |
| Jul 7, 2021 at 20:16 | comment | added | Andrea Marino | If you suspect the sequence hits infinitely many times a number, it seems like $n$ will be "random" modulo $i+1$ with respect to $a_i$. Say you have just hit $a$. If $i$ is big and we have to wait a bit to hit a number divisible by $i+1$, you will have: $a, r-a, a+1, r-a+1, a+2, r-a+2 \ldots$ where $r$ is a "big" random number. Since you have the code, I would suggest to test the sequence with random numbers (increasingly bigger) to better reproduce the 'definitive regime'. If explicit arithmetic properties of that n are necessary I guess it's a hard problem. | |
| Jul 7, 2021 at 19:56 | history | edited | Alkan | CC BY-SA 4.0 |
I update experimental range that I observe.
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| Jul 1, 2021 at 12:49 | history | edited | Alkan | CC BY-SA 4.0 |
I added currently accepted sequence entries and I edited a typo (hits-->hit)
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| Jun 29, 2021 at 18:30 | history | asked | Alkan | CC BY-SA 4.0 |