10 bit PWM on Arduino UNO
On your code, you using analogRead but declaring the pin (A3) as output. Change it to pinMode(A3,INPUT);

Aside from that, PWM is basically a digital output which changing (HIGH and LOW) at specified frequency. When the result you got is 


  0 0 1022 1021 0 1022 1021 0 0 1021 0 1021 1021 0 0 1021 0 0 1022


There's nothing wrong. 0 --> LOW, and 1021++ --> HIGH
If you want "measure" something from the PWM, use pulseIn() instead, you can check the documentation here.    

If you want to measure the PWM value, I suggest you read:
Can I connect a PWM pin on one Arduino to an analog input on another?