tea.mathoverflow.net - Discussion Feed (Ratio of positive integers of a specific recursion) Sun, 04 Nov 2018 16:07:38 -0800 http://mathoverflow.tqft.net/ Lussumo Vanilla 1.1.9 & Feed Publisher Vassilis Parassidis comments on "Ratio of positive integers of a specific recursion" (17890) http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17890#Comment_17890 http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17890#Comment_17890 Fri, 23 Dec 2011 19:29:57 -0800 Vassilis Parassidis Vassilis Parassidis comments on "Ratio of positive integers of a specific recursion" (17871) http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17871#Comment_17871 http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17871#Comment_17871 Fri, 23 Dec 2011 07:54:11 -0800 Vassilis Parassidis
Thank you for your helpful comments. I will edit the formatting. I think "(e.g X=Y, Z=W, V=a_n)" would complicate the question

Vassili ]]> Vassilis Parassidis comments on "Ratio of positive integers of a specific recursion" (17870) http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17870#Comment_17870 http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17870#Comment_17870 Fri, 23 Dec 2011 07:48:34 -0800 Vassilis Parassidis
I thought that because I was suspended, members had considered the previous post closed. Because I am looking for answers I thought asking again was the right way to reopen the discussion. I certainly did not intend to spam the site.

Sincerely,
Vassili ]]> Scott Morrison comments on "Ratio of positive integers of a specific recursion" (17869) http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17869#Comment_17869 http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17869#Comment_17869 Fri, 23 Dec 2011 07:16:27 -0800 Scott Morrison Dear Vassilis,

Unless I am mistaken, this is a duplicate of your previous post on meta. Do you understand that I see this as spamming our site, and extremely unwelcome?

Sincerely, Scott Morrison

]]> grp comments on "Ratio of positive integers of a specific recursion" (17866) http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17866#Comment_17866 http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17866#Comment_17866 Fri, 23 Dec 2011 00:48:41 -0800 grp <BEGIN FORMAT>
Is the following question acceptable for posting on MathOverflow?

<body of question>

If it is not acceptable, how can it be improved?
<END FORMAT>

Your current question looks clear and understandable, except the formatting on meta makes it unclear to me whether
it is two sets of three equations each (e.g X=Y, Z=W, V=a_n) , or two sets of multiple relations (e.g. X=Y=Z=a_n). To answer your question, you might consider drawing some kind of phase diagram for a system related to these recurrences like (x,y) goes (xm^i +a ,ym^i +b), and see if such a picture offers insight. Also, you might ask the question slightly differently, as in "Can one find the set of initial values (a_0,k_0,a_1,k_1) so that the sequence of values (k_n/a_n) converges, and can that limit of convergence be easily expressed in terms of the initial values?"

Gerhard "Ask Me About System Design" Paseman, 2011.12.23 ]]> Vassilis Parassidis comments on "Ratio of positive integers of a specific recursion" (17864) http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17864#Comment_17864 http://mathoverflow.tqft.net/discussion/1260/ratio-of-positive-integers-of-a-specific-recursion/?Focus=17864#Comment_17864 Thu, 22 Dec 2011 21:11:56 -0800 Vassilis Parassidis a_1m^1+a_0=a_2, a_2m^2+a_1=a_3, a_n-1m^(n-1)+a_n-2=a_n
k_1m^1+k_0=k_2, k_2m^2+k_1=k_3, k_n-1m^(n-1)+k_n-2=k_n.
For m any non-zero positive integer and a_0=1, a_1=0, k_0=0, k_1=1 I was able to predict the result of k_n/a_n. For any other pair of values a_0≠a_1 and k_0≠k_1 the result is unpredictable. Does anyone know if it is possible to predict the numerical value of the ratio k_n/a_n for such pairs?
If the question is not acceptable, how can I improve it? ]]>