#Mathematica, 109 bytes
s={};For[i=2,1<2,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;Echo@i]]
Continuously output terms of the sequence
#Mathematica, 109 bytes
s={};For[i=2,1<2,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;Echo@i]]