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 A327106 BII-numbers of set-systems with maximum degree 2. 2
 5, 6, 7, 13, 14, 15, 17, 19, 20, 22, 24, 25, 26, 27, 28, 30, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 65, 66, 67, 68, 72, 73, 74, 75, 76, 80, 82, 96, 97, 133, 134, 135, 141, 142, 143, 145, 147, 148, 150, 152, 153, 154, 155, 156, 158, 162 (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 2 together with their BII-numbers begins:    5: {{1},{1,2}}    6: {{2},{1,2}}    7: {{1},{2},{1,2}}   13: {{1},{1,2},{3}}   14: {{2},{1,2},{3}}   15: {{1},{2},{1,2},{3}}   17: {{1},{1,3}}   19: {{1},{2},{1,3}}   20: {{1,2},{1,3}}   22: {{2},{1,2},{1,3}}   24: {{3},{1,3}}   25: {{1},{3},{1,3}}   26: {{2},{3},{1,3}}   27: {{1},{2},{3},{1,3}}   28: {{1,2},{3},{1,3}}   30: {{2},{1,2},{3},{1,3}}   34: {{2},{2,3}}   35: {{1},{2},{2,3}}   36: {{1,2},{2,3}}   37: {{1},{1,2},{2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Select[Range[0, 100], If[#==0, 0, Max@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]]==2&] CROSSREFS Positions of 2's in A327104. Graphs with maximum degree 2 are counted by A136284. Cf. A000120, A048793, A058891, A070939, A326031, A326701, A326786, A327041, A327103. Sequence in context: A011761 A106745 A165776 * A003273 A006991 A047574 Adjacent sequences:  A327103 A327104 A327105 * A327107 A327108 A327109 KEYWORD nonn AUTHOR Gus Wiseman, Aug 26 2019 STATUS approved

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)