Question

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),...

Answer 1

perhaps whenever x is odd add one to y ?

Answer 2

..or you want an equation?

Answer 3

\(\Large \color{purple}{ 1) x + 1,y + 1 }\)
\(\Large \color{purple}{ 2) x + 1, y }\)

It keeps repeating.

Answer 4

and expression for the n-th term.

Answer 5

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

Answer 6

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

Answer 7

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?)

Answer 8

@TuringTest lol, Do - while is in every language

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

thank you both.

Answer 13

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

Answer 14

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 =/

Answer 15

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

Answer 16

if we ratio it out:

\[1,2,1\frac{1}{2},2,1\frac{1}{3},2,1\frac{1}{4},2,1\frac{1}{5},2,1\frac{1}{6},...\]

Answer 17

\[f(x')=1+\frac{1}{x};\ x\in Odd\]\[f(x')=2;\ x\in Even\]

prolly bad notations, but the slope of each discrete point would be something like this

Answer 18

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

Answer 19

Thank you amistre64 I'll try to understand that.

Answer 20

I just th

Answer 21

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

Answer 22

computers are great with piecewises ;) good luck with it

Answer 23

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

Answer 24

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

Answer 25

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