Return to Answer

#Mathematica, 109 94 bytes

s={};Do[!SubsetQ[s,(t=Subsequences@IntegerDigits[i,2])[[2;;-2]]]&&(s=s~Join~t;Echo@i),{i,∞}]

Continuously output terms of the sequence

Special thanx to @ngenisis for -15 bytes

#Mathematica, 128 bytes

(s=r={};For[i=2,i<2#,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;r~AppendTo~i]];r[[#]])&

Take n as input and generate the nth term in this sequence (1 indexed)

input

[1000]

output

1342

#Mathematica, 109 94 bytes

s={};Do[!SubsetQ[s,(t=Subsequences@IntegerDigits[i,2])[[2;;-2]]]&&(s=s~Join~t;Echo@i),{i,∞}]

Continuously output terms of the sequence

Special thanx to @ngenisis for -15 bytes

#Mathematica, 123 bytes

(s=r={};For[i=2,i<2#,i++,If[!ContainsAll[s,(t=Subsequences@IntegerDigits[i,2])[[2;;-2]]],s=s~Join~t;r~AppendTo~i]];r[[#]])&

Take n as input and generate the nth term in this sequence (1 indexed)

input

[1000]

output

1342

#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

here is a version that has 0.2 sec delay between the results in order to be easier for you to follow... Press alt+. to abort

s={};For[i=2,1<2,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;Echo@i;[email protected]]]  

#Mathematica, 128 bytes

(s=r={};For[i=2,i<2#,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;r~AppendTo~i]];r[[#]])&

Take n as input and generate the nth term in this sequence (1 indexed)

input

[1000]

output

1342

#Mathematica, 109 94 bytes

s={};Do[!SubsetQ[s,(t=Subsequences@IntegerDigits[i,2])[[2;;-2]]]&&(s=s~Join~t;Echo@i),{i,∞}]

Continuously output terms of the sequence

Special thanx to @ngenisis for -15 bytes

#Mathematica, 128 bytes

(s=r={};For[i=2,i<2#,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;r~AppendTo~i]];r[[#]])&

Take n as input and generate the nth term in this sequence (1 indexed)

input

[1000]

output

1342

#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, 128 bytes

(s=r={};For[i=2,i<2#,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;r~AppendTo~i]];r[[#]])&

Take n as input and generate the nth term in this sequence (1 indexed)

#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

here is a version that has 0.2 sec delay between the results in order to be easier for you to follow... Press alt+. to abort

s={};For[i=2,1<2,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;Echo@i;[email protected]]]  

#Mathematica, 128 bytes

(s=r={};For[i=2,i<2#,i++,If[!ContainsAll[s,Union[t=Subsequences@IntegerDigits[i,2]][[2;;-2]]],s=s~Join~t;r~AppendTo~i]];r[[#]])&

Take n as input and generate the nth term in this sequence (1 indexed)

input

[1000]

output

1342