Print the Nth non-palindromic number

Pyth, 7 bytes

e.f!_I`

Test suite

Explanation:

e.f!_I`
e.f!_I`ZQ    Implicit variable introduction.
 .f     Q    Find the first Q numbers whether the following is truthy,
             starting at 1, where Q is the input.
      `Z     Convert the number to a string.
     _I      Check if it's the same when reversed.
    !        Logical not.
 e           Return the last element of the list.

Haskell, 38 bytes

([x|x<-[1..],(/=)<*>reverse$show x]!!)

Uses 0-based index. ([x|x<-[1..],(/=)<*>reverse$show x]!!) 11 -> 23.

The test whether to keep a number (/=)<*>reverse$show x translates to (show x) /= (reverse (show x)), i.e check if the string representation of the number does not equal the reverse of the string representation.

Brachylog, 14 11 bytes

;0{<≜.↔¬}ⁱ⁽

-3 bytes tanks to Fatalize

Explanation

; {      }ⁱ⁽        --  Find the nth number
 0                  --      (starting with 0)
   <                --      which is bigger then the previous one
    ≜               --      make explicit (otherwise it fucks up)
      .             --      which is the output
       ↔            --      and if reversed
        ¬           --      is not the output

Try it online!