Simple logic circuit to filter out the even numbered pulse?
Take the output of a divide-by-2 circuit and feed it back alongside the original signal into a two-input AND gate:


your input signal is tied to both the input of the divide-by-2 circuit and one of the inputs of the AND gate,
the output of the divide-by-2 circuit is tied to the other input of the AND gate,
the output of the AND gate gives you the result.


That way the pulse width will remain as it is in the input.