Figure 1 shows the problem that confronted me over the breakfast table this morning.
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Figure 1 |
As I've said before, I dislike this format and what we should say is that we say that we have a function \(f(x)\) that maps \(x\) to \(y\):
- \(f(1)=3\)
- \(f(2)=3\)
- \(f(3)=5\)
- \(f(4)=4\)
- \(f(5)=4\)
- \(f(6)= \, \, ?\)
I'll make a small adjustment here so that the graph has \(x\) coordinates that correspond. It looks like this with the answer of \(f(6)=6\) added which I'll explain and Figure 1 shows the result:
- \(f(0)=1\)
- \(f(1)=3\)
- \(f(2)=3\)
- \(f(3)=5\)
- \(f(4)=4\)
- \(f(5)=4\)
- \(f(6)= 6 \)
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Figure 1: permalink |
As can be seen from the graph the pattern repeats once \( (5, 4) \) is reached. Figure 2 is the pattern expanded.
What is the formula to represent the numbers as part of a recurrent series given by \( a(n) \) = ... ? Can the graph be expressed in terms of \(y=f(x) \) for some function \(f\)? These are two interesting questions that I should try to answer. Once I crack it, I'll post the information here and maybe a link to a new blog post about how I cracked it.
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Figure 2: permalink |
What is the formula to represent the numbers as part of a recurrent series given by \( a(n) \) = ... ? Can the graph be expressed in terms of \(y=f(x) \) for some function \(f\)? These are two interesting questions that I should try to answer. Once I crack it, I'll post the information here and maybe a link to a new blog post about how I cracked it.
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