- anonymous

What is the rule to get this list of ordered pairs :
(0,0),(1,1),(2,1),(3,2),(4,2),(5,3),(6,3),...

- katieb

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- TuringTest

perhaps whenever x is odd add one to y ?

- TuringTest

..or you want an equation?

- ParthKohli

\(\Large \color{purple}{ 1) x + 1,y + 1 }\)
\(\Large \color{purple}{ 2) x + 1, y }\)
It keeps repeating.

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## More answers

- anonymous

and expression for the n-th term.

- anonymous

Well I actually got it from a while loop, and I wanted to know if I can translate it to a mathematical expression.

- ParthKohli

No, you have to use the programming if - else, or while - do

- TuringTest

should be like (n,n/2) when n is even
and (n,n/2+1) when n is odd
how to combine them
(you using python?)

- ParthKohli

@TuringTest lol, Do - while is in every language

- TuringTest

I ask because I am learning python and wanted tips if No-Data is an expert
..sort of a separate Q

- anonymous

This is what it does:
x = 0, y = 0
y = x - y
x = x + 1

- anonymous

Sorry Turing I'm not a expert, I'm actually learning some Java, but I got distracted with this thing hehe.

- anonymous

thank you both.

- amistre64

what you have typed up is already a recurrsive definition; and it might have to be piecewise defined to be explicit as has already been pointed out

- anonymous

There is no way of expressing it without in the piecewise way?. I'm so fool because I can't see it from the code =/

- amistre64

if you are trying to confine yourself to a limited method, your going to be limited in your results ....
the piecewise functions are real and useable function ...
as is it looks like y is increaseing at half the rate of x, and if you can use a ceiling or floor function to weed it up or down as needed, you might be able to code it up sufficiently with a 0,0 condition as separate

- amistre64

if we ratio it out:
\[1,2,1\frac{1}{2},2,1\frac{1}{3},2,1\frac{1}{4},2,1\frac{1}{5},2,1\frac{1}{6},...\]

- amistre64

\[f(x')=1+\frac{1}{x};\ x\in Odd\]\[f(x')=2;\ x\in Even\]
prolly bad notations, but the slope of each discrete point would be something like this

- amistre64

1 + 1/n maybe better; for x in Odd

- anonymous

Thank you amistre64 I'll try to understand that.

- anonymous

I just th

- anonymous

I just thought it would be easier to do without piecewise functions, but now I see it is not.

- amistre64

computers are great with piecewises ;) good luck with it

- TuringTest

sorry no-Data I had to take your medal away and give it to amistre... his was the best answer :P

- anonymous

No problem TuringTest I actually was asking for an answer and that is what amistre64 gave me.

- anonymous

Although I didn't know someone could change his mind about a medal.

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