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.
%I A309274 #35 Aug 03 2019 02:45:54
%S A309274 0,1,3,7,11,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,
%T A309274 151,159,167,175,183,191,199,207,215,223,231,239,247,255,267,271,287,
%U A309274 303,319,335,351,367,383,399,415,431,447,463,479,495,511,523,527,543
%N A309274 Ackermann Coding (BIT predicate) of transitive hereditarily finite sets.
%C A309274 If the representation of a(n) in base 2 contains the k-th bit (2^k), then it must contain the bits of k.
%C A309274 A034797 is a subsequence, and can be seen as a recursive variant of this sequence. - _Rémy Sigrist_, Jul 25 2019
%H A309274 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hereditarily_finite_set">Hereditarily finite set</a>
%H A309274 Wikipedia, <a href="https://en.wikipedia.org/wiki/Transitive_set">Transitive set</a>
%e A309274 23 is in the sequence because 23 = 2^4 + 2^2 + 2^1 + 2^0 encodes the transitive set {0,1,{1},{{1}}} (remember that 0 is the empty set and 1 is {0}).
%t A309274 b[n_] := (Flatten @ Position[Reverse[IntegerDigits[n, 2]], 1] - 1);
%t A309274 okQ[n_] := With[{bb = b[n]}, AllTrue[b /@ bb, Intersection[bb, #] == #&]];
%t A309274 Select[Range[0, 600], okQ] (* _Jean-François Alcover_, Jul 25 2019 *)
%o A309274 (PARI) is(n) = { for (b=0, #binary(n), if (bittest(n, b), if (bitand(n, b)!=b, return (0)))); return (1) } \\ _Rémy Sigrist_, Jul 25 2019
%Y A309274 Cf. A034797, A102553.
%K A309274 nonn
%O A309274 1,3
%A A309274 _Christophe Papazian_, Jul 24 2019