Generate unseen numbers
Python 3, 88 80 78 75 bytes

-6 bytes thanks to Wheat Wizard
-2 bytes thanks to RootTwo
-3 bytes thanks to notjagan


s={0}
n=1
while 1:n+=1;b=f"{n:b}";p={b[1:],b[:-1]};s|=p-s and{b,print(n)}|p


Try it online!