## No-data 3 years ago 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),...

1. TuringTest

perhaps whenever x is odd add one to y ?

2. TuringTest

..or you want an equation?

3. ParthKohli

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

4. No-data

and expression for the n-th term.

5. No-data

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

6. ParthKohli

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

7. 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?)

8. ParthKohli

@TuringTest lol, Do - while is in every language

9. TuringTest

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

10. No-data

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

11. No-data

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

12. No-data

thank you both.

13. 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

14. No-data

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 =/

15. 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

16. amistre64

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

17. 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

18. amistre64

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

19. No-data

Thank you amistre64 I'll try to understand that.

20. No-data

I just th

21. No-data

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

22. amistre64

computers are great with piecewises ;) good luck with it

23. TuringTest

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

24. No-data

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

25. No-data

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