This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a = {1}; b = {1}; Do[k = b[[i - 1]] + 1; While[SequenceCount[Flatten@ a, Set[d, Reverse@ IntegerDigits[k, 2]]] != 0, k++]; a = Join[a, d]; AppendTo[b, k], {i, 2, 59}]; b (* Michael De Vlieger, Aug 21 2017 *)
A118252(n,show=0,a=1)={my(c=[a],S=[],L); for(k=1,n, show & print1(a","); while( setsearch(S,binary(a++)),); c=concat(binary(a),c); S=[]; for(i=0,#c-L=#binary(a), c[i+1] & for(j=i+L,min(i+L+1,#c), S=setunion(S,Set(t=[vecextract(c,2^j-2^i)])))));a} \\ M. F. Hasler, Dec 29 2012
5 is not a term since its binary expansion is "101", which is the concatenation of earlier a(2)="10" and a(1)="1". 19 is not a term since its binary expansion is "10011", which is the concatenation of a(4)="100" and a(3)="11".
conc[x_, y_] := FromDigits[Flatten@IntegerDigits[{x, y}, 2], 2]; a[1] = 1; a[n_] := a[n] = Module[{k = a[n - 1] + 1, v = Array[a, n - 1], c}, c = conc @@@ Select[Tuples[v, {2}], UnsameQ @@ # &]; While[! FreeQ[c, k], k++]; k]; Array[a, 60] (* Amiram Eldar, Sep 29 2023 *)
from itertools import islice
def agen(): # generator of terms
an, bins, concats = 1, {"1"}, set()
while True:
yield an
while (bn:=bin(an:=an+1)[2:]) in concats: pass
concats |= {bn+bi for bi in bins} | {bi+bn for bi in bins}
bins.add(bn)
print(list(islice(agen(),62))) # Michael S. Branicky, Sep 29 2023
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