Someone2841
New member
- Joined
- Sep 7, 2011
- Messages
- 35
The table below represents a series of repeating patterns of \(\displaystyle p-2\) dashes followed by \(\displaystyle 2\) zeroes; it is implied by the \(\displaystyle \dots\) that that same pattern continues ad infinitum.
\(\displaystyle \begin{matrix}
&n & 1 & 2 & 3 & 4 & 5 & 6 & 7\\
p\\
3&&- & 0 & 0 &\dots&&&\\
5&&- & - & - & 0 & 0 &\dots\\
7&&- & - & - & - & - & 0 & 0 \dots\\
\end{matrix}\)
Where n is the position of the sequence. My question is: What is the minimum value of n such that all columns are 0?
In this example, the answer can be found by brute force as being \(\displaystyle n=14\). What I am looking for is a solution for a more general case. In particular, I am looking for a solution for an array of coprime p's which each have only one prime factor (i.e., an array of coprime prime powers). I've been working with this for a while, but seem to have had no real progress. Does anyone have, if not an explicit or implicit solution, a general method (or even field of analysis) to tackle this problem?
\(\displaystyle \begin{matrix}
&n & 1 & 2 & 3 & 4 & 5 & 6 & 7\\
p\\
3&&- & 0 & 0 &\dots&&&\\
5&&- & - & - & 0 & 0 &\dots\\
7&&- & - & - & - & - & 0 & 0 \dots\\
\end{matrix}\)
Where n is the position of the sequence. My question is: What is the minimum value of n such that all columns are 0?
In this example, the answer can be found by brute force as being \(\displaystyle n=14\). What I am looking for is a solution for a more general case. In particular, I am looking for a solution for an array of coprime p's which each have only one prime factor (i.e., an array of coprime prime powers). I've been working with this for a while, but seem to have had no real progress. Does anyone have, if not an explicit or implicit solution, a general method (or even field of analysis) to tackle this problem?