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 A327376 #4 Sep 09 2019 12:05:28
%S A327376 2868,2869,2870,2871,2876,2877,2878,2879,2880,2881,2882,2883,2884,
%T A327376 2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,
%U A327376 2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914
%N A327376 BII-numbers of set-systems with vertex-connectivity 3.
%C A327376 A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every set-system (finite set of finite nonempty sets) has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18. Elements of a set-system are sometimes called edges.
%C A327376 The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.
%e A327376 The sequence of all set-systems with vertex-connectivity 3 together with their BII-numbers begins:
%e A327376 2868: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2869: {{1},{1,2},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2870: {{2},{1,2},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2871: {{1},{2},{1,2},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2876: {{1,2},{3},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2877: {{1},{1,2},{3},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2878: {{2},{1,2},{3},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2879: {{1},{2},{1,2},{3},{1,3},{2,3},{1,4},{2,4},{3,4}}
%e A327376 2880: {{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2881: {{1},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2882: {{2},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2883: {{1},{2},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2884: {{1,2},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2885: {{1},{1,2},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2886: {{2},{1,2},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2887: {{1},{2},{1,2},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2888: {{3},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2889: {{1},{3},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2890: {{2},{3},{1,2,3},{1,4},{2,4},{3,4}}
%e A327376 2891: {{1},{2},{3},{1,2,3},{1,4},{2,4},{3,4}}
%t A327376 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A327376 csm[s_]:=With[{c=Select[Subsets[Range[Length[s]],{2}],Length[Intersection@@s[[#]]]>0&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A327376 vertConnSys[vts_,eds_]:=Min@@Length/@Select[Subsets[vts],Function[del,Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds,Alternatives@@del,{2}],{}]]!={Complement[vts,del]}]];
%t A327376 Select[Range[0,3000],vertConnSys[Union@@bpe/@bpe[#],bpe/@bpe[#]]==3&]
%Y A327376 Positions of 3's in A327051.
%Y A327376 BII-numbers for vertex-connectivity 2 are A327374.
%Y A327376 BII-numbers for spanning edge-connectivity >= 3 are A327110.
%Y A327376 The enumeration of labeled graphs by vertex-connectivity is A327334.
%Y A327376 Cf. A000120, A013922, A048793, A070939, A259862, A323818, A326031, A326753, A326786, A327375.
%K A327376 nonn
%O A327376 1,1
%A A327376 _Gus Wiseman_, Sep 05 2019