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 A327107 BII-numbers of set-systems with minimum vertex-degree > 1. 5
 7, 25, 30, 31, 42, 45, 47, 51, 52, 53, 54, 55, 59, 60, 61, 62, 63, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 97, 99, 100, 101, 102, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. In a set-system, the degree of a vertex is the number of edges containing it. LINKS EXAMPLE The sequence of all set-systems with maximum degree > 1 together with their BII-numbers begins:    7: {{1},{2},{1,2}}   25: {{1},{3},{1,3}}   30: {{2},{1,2},{3},{1,3}}   31: {{1},{2},{1,2},{3},{1,3}}   42: {{2},{3},{2,3}}   45: {{1},{1,2},{3},{2,3}}   47: {{1},{2},{1,2},{3},{2,3}}   51: {{1},{2},{1,3},{2,3}}   52: {{1,2},{1,3},{2,3}}   53: {{1},{1,2},{1,3},{2,3}}   54: {{2},{1,2},{1,3},{2,3}}   55: {{1},{2},{1,2},{1,3},{2,3}}   59: {{1},{2},{3},{1,3},{2,3}}   60: {{1,2},{3},{1,3},{2,3}}   61: {{1},{1,2},{3},{1,3},{2,3}}   62: {{2},{1,2},{3},{1,3},{2,3}}   63: {{1},{2},{1,2},{3},{1,3},{2,3}}   75: {{1},{2},{3},{1,2,3}}   76: {{1,2},{3},{1,2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Select[Range[100], Min@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]>1&] CROSSREFS Positions of terms > 1 in A327103. BII-numbers for minimum degree 1 are A327105. Graphs with minimum degree > 1 are counted by A059167. Cf. A000120, A029931, A048793, A058891, A070939, A245797, A326031, A326701, A326786, A327041, A327104, A327227-A327230. Sequence in context: A034125 A196013 A272366 * A075926 A065660 A100496 Adjacent sequences:  A327104 A327105 A327106 * A327108 A327109 A327110 KEYWORD nonn AUTHOR Gus Wiseman, Aug 26 2019 STATUS approved

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)