Timeline for Simplification of the closed form for the A329369
Current License: CC BY-SA 4.0
9 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Jul 9 at 17:34 | vote | accept | Notamathematician | ||
Jul 9 at 15:12 | answer | added | Max Alekseyev | timeline score: 4 | |
Jul 7 at 13:54 | comment | added | მამუკა ჯიბლაძე | Also above million, there are $a(2498)=a(3014)=a(17414)=a(20462)=1526775$ and $a(13140)=a(13644)=a(267678)=a(275134)=184481855$. Most probably there will be larger and larger $a$-preimages further | |
Jul 7 at 13:49 | comment | added | მამუკა ჯიბლაძე | Oh sorry! Indeed $a(1208)=a(1814)=a(131072)=a(262142)=262143$ | |
Jul 7 at 13:02 | comment | added | Notamathematician | @მამუკაჯიბლაძე, please double check your result. | |
Jul 7 at 12:41 | comment | added | მამუკა ჯიბლაძე | Not sure about that, I can only confirm that $a(2n)=a(\tau(2n))$ where binary digits of $\tau(x)$ are $1-\text{reversed binary digits of $x$}$ | |
Jul 7 at 12:34 | comment | added | Notamathematician | @მამუკაჯიბლაძე, it looks like we can permute $a(2n)$ with A059894 and it gives no changes. So A035928 is the double of its fixed points (A290254). | |
Jul 7 at 9:55 | comment | added | მამუკა ჯიბლაძე | Some fun facts. Up to $n=$ one million, for most values of $a(n)$ there are exactly two even $n$ with this value. Only for the value $31$ there are three $n$ with this value of $a(n)$, namely $a(12)=a(16)=a(30)=31$. Those even $n$ for which no other even $n$ attains the same value are $2,10,38,42,52,56,142,...$; except for one term, namely 12, this is A035928. These are the only possibilities, i. e. up to one million, number of the even $n$ with the same value of $a(n)$ is either 3 (only for $a(n)=31$), 1 (for $n$ in A035928), or 2 (in all remaining cases) | |
Jul 7 at 6:13 | history | asked | Notamathematician | CC BY-SA 4.0 |