From the results how to find the formula behind a sequence? From the following table how can I find the formula to reproduce this results, given that X is between the indicated range on the left column? 

 A: You can try this define the following function 
$$f(x) =  \left\lfloor \frac{x-10}{10 + ( -1)^{g(x)}} \right \rfloor+1$$
Where $g(x)$ values either $0$ or $1$ 
\begin{cases} 1 &, x\in (10,18) \\ 0 &,x\in (19,29) \\ 1 &, x\in (30,38) \\ \vdots \end{cases}
you can think about the functions in the type of $\lfloor \sin ( x + c \sin x ) \rfloor$. Where the $\lfloor \rfloor$ is the floor function ( greatest integer ). We want a periodic function with unequal interval seizes. Check this 
Asymmetric periods in a sine curve. Try for example this $$ \operatorname{floor}\left(2\sin\left(\frac{\pi}{4}\ +\ \frac{\pi}{4}\sin\left(\frac{x-0.97}{2.6}\right)\right)\right)$$
you need to play with such functions. 
A: There is no particular formula of this series
It just follows a pattern, that's it.
Anyways I can give you a continuation of the pattern.
In the column X
You add 8 to every 2n+1 terms for n being a whole number.
You add 10 to every 2n terms for n being a whole number.
Remember to add 1 to the maximum value of the preceding range.
In Results Column
You add 1 sequentially for the corresponding X range.
