Timeline for Golomb subsets of $\mathbb{N}$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27 at 19:35 | comment | added | მამუკა ჯიბლაძე | As for A247556, it does answer the question but is constructed in a different way: let $n$ be as above for $\{a(1),...,a(k-1)\}$. If $\{a(1),...,a(k-1),a(k-1)+n\}$ is Golomb then one puts $a(k)=a(k-1)+n$. Otherwise one puts $a(k)=a(k-1)+r$ and $a(k+1)=a(k)+n$ where $r$ is the smallest number with $\{a(1),...,a(k-1),a(k-1)+r,a(k-1)+r+n\}$ Golomb. The result is still different from what I get, it seems to be more economic, as it omits e. g. $1404, 1772, 1820, 2161, 2210, 2514, 2565, 3004, 3059, 3503, 3560, 4006, 4067, 4447, 4514, 5280, 5350, 5677, 5748,...$ | |
| Jun 27 at 19:25 | comment | added | მამუკა ჯიბლაძე | Interestingly, A005282 does not answer the question, as its $\mathrm{dist}$ omits A080200 - namely, $33, 88, 98, 99, 105, 106, 112, 126, 130, 132, 134, 150, 152, 154, 156,...$ | |
| Jun 27 at 19:14 | comment | added | მამუკა ჯიბლაძე | See also A005282: $a(n)$ is the smallest number $>a(n-1)$ such that $\{a(1),...,a(n)\}$ is Golomb. It goes $1,2,4,8,13,21,31,45, 66, 81, 97, 123, 148, 182, 204, 252, 290, 361, 401, 475, 565, 593, 662, 775, 822, 916, 970, 1016, 1159, 1312,...$ | |
| Jun 27 at 18:13 | comment | added | მამუკა ჯიბლაძე | Sorry I thought I checked it but cannot reproduce it anymore. After $\{1,2\}$ I obtain $\{1,2,4\}$. Indeed $\operatorname{dist}(\{1,2\})=\{1\}$, so $n=2$, and for $m=1$ I get $\{1,2\}\cup\{1,3\}=\{1,2,3\}$ which is not Golomb, while for $m=2$ I get $\{1,2\}\cup\{2,4\}=\{1,2,4\}$ which is Golomb. In this way I obtain $\{1,2,4,8,13,21,31,45,66,81,97,144,166,200,225,307,333,416,444,592,625,679,717,935,974,1135,1175,...\}$ (which is also not on OEIS) | |
| Jun 22 at 23:22 | comment | added | მამუკა ჯიბლაძე | Why not add it to OEIS then? It surely deserves it! | |
| Jun 21 at 20:59 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo
|
| Jun 21 at 18:48 | vote | accept | Dominic van der Zypen | ||
| Jun 21 at 14:42 | history | edited | YCor | CC BY-SA 4.0 |
added computations
|
| Jun 21 at 14:26 | history | answered | YCor | CC BY-SA 4.0 |