Is $L= \{ a^ib^j \mid j\neq i \ and \ j\neq2i \ \} $ context free? $L = \{ a^ib^j \mid j\neq i \ and \ j\neq2i \ \} $

Is this language a context free language?
If yes give a PDA. If no, give a proof.

The pumping lemma for context free languages doesn't seem to work here.

Let $p&gt;1$ be the pumping length. Let the string be divided into five parts according to pumping lemma as $w = uvxyz$.

For any string of the form $a^ib^j \ s.t.$: 


$ j\lt i-1$ choose $v=a, \ x=\epsilon, \ y=\epsilon$
$ j\gt 2i+1$ choose $v=\epsilon, \ x=\epsilon, \ y=b$
$ j = i-1$ choose $v=a, \ x=\epsilon, \ y=b$
$ j =  2i+1$ choose $v=a, \ x=\epsilon, \ y=b$
$ j\gt i,\ j\lt 2i $ choose $v=a, \ x=\epsilon, \ y=b$
It is context Free.

You can see it as a union of two languages:
$L_1$ where $j&gt;2i$ and $L_2$ which is very similar to the one of this question.

More information you can find in this question.