there are more things messed up...

first by using a+=pulse inside your rect you dont only define the width/height but also add pulse to a

then you check if a == 1;
but you already start with 50, so it never gets 1.

anyway i would do it different

define your size ( could be a in your case) and a pulse variable.
you already did that.

now, only change the pulse and add it to a inside the rect command

now we need to change the pulsing. you could add up 1 like you tried. but if you want to get much smoother results you could make use of a sin function that always changes between -1 and 1

use frameCount as it is a counter we can easily make use of for the sin.

void draw(){
 smooth();
rectMode(CENTER);
background(0);
float a = 10;
float pulse = abs(sin(frameCount/20.0))*10.0; //20 is pulse speed. 10 is the resizing when pulsing
rect(50,50,a+pulse,a+pulse);

}