Timeline for Finding integers whose sum of digits equals the sum of the digits of a multiple of them
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 7, 2019 at 2:00 | review | Close votes | |||
| Sep 11, 2019 at 3:05 | |||||
| Sep 7, 2019 at 0:23 | comment | added | Gerry Myerson | The list of integers $a$ such that the digit sums of $a$ and $7a$ are equal begins with $3,6,9,15,18,30,33,36,39,45,48,60,63\dots$. Neither this sequence, nor the one you get by dividing each term by three, is in the OEIS. | |
| Sep 6, 2019 at 17:15 | history | edited | Guntram | CC BY-SA 4.0 |
clarified the question according to the comments
|
| May 5, 2010 at 20:58 | vote | accept | Jull | ||
| May 5, 2010 at 10:46 | comment | added | Wadim Zudilin | @Yemon: Allright. I still hope that the author is interested in explaining what's the problem is about. Maybe, even what it's for. | |
| May 5, 2010 at 9:51 | comment | added | Yemon Choi | @Wadim: I just removed a tag that didn't belong there | |
| May 5, 2010 at 9:25 | answer | added | Wadim Zudilin | timeline score: 1 | |
| May 5, 2010 at 9:19 | comment | added | Wadim Zudilin | @Yemon: The problem is still trivial. What was the edit?! | |
| May 5, 2010 at 8:20 | history | edited | Yemon Choi |
removed irrelevant comm alg tag
|
|
| May 5, 2010 at 6:04 | comment | added | Wadim Zudilin | @Jull: It could be nice if you edit your problem more. If you wish to get the property $S(a)=S(xa)$ valid for all $x>0$. Then there are no such numbers. Indeed, if $a$ exists, then concantination $\overline{aa}=a\cdot$ with $x=10^n+1$ gives you a number with sum of digits twice more than $S(a)$. If you mean a fixed given $x$, then you can reduce your check using the fact that $S(a)$ and $a$ have the same residue modulo 9, so that $ax$ and $x$ has to be congruent modulo 9. | |
| May 5, 2010 at 4:06 | answer | added | ogerard | timeline score: 2 | |
| May 5, 2010 at 2:47 | history | edited | Jull | CC BY-SA 2.5 |
added 1 characters in body; edited tags
|
| May 5, 2010 at 2:35 | comment | added | Jull | thanks for clarification. I probably didn't explain it properly. Range doesn't matter, it's much bigger and brute force won't help (my code is already running for 3 days). So, I decided to look for more reasonable solution... | |
| May 4, 2010 at 23:52 | comment | added | Zev Chonoles | Thanks for the clarification Wadim, it makes much more sense now. | |
| May 4, 2010 at 23:49 | comment | added | Wadim Zudilin | The problem is: For a given integer $x>0$, find all numbers $a$ in the range such that the digit sums of $a$ and $xa$ coincide. | |
| May 4, 2010 at 23:47 | comment | added | Mariano Suárez-Álvarez | Can't you take $x=10$ for all $a$'s? I guess I do not understand the problem... | |
| May 4, 2010 at 23:46 | comment | added | Zev Chonoles | Wouldn't $a_1=1$, $x=10$ work? Also, where do the $a_2,\ldots,a_n$ come in? Presumably, you meant that the digit sum of $a_i$ is equal to the digit sum of $x\cdot a_{i-1}$. However, I'm not sure this is appropriate for MO, please see the FAQ mathoverflow.net/faq#whatnot for a list of some other sites for which your question may be better suited. | |
| May 4, 2010 at 23:43 | comment | added | Wadim Zudilin | For this tiny range you may simply program verification of the property. | |
| May 4, 2010 at 23:30 | history | asked | Jull | CC BY-SA 2.5 |