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 A326785 BII-numbers of uniform regular set-systems. 5
 0, 1, 2, 3, 4, 8, 9, 10, 11, 16, 32, 52, 64, 128, 129, 130, 131, 136, 137, 138, 139, 256, 288, 512, 528, 772, 816, 1024, 2048, 2052, 2320, 2340, 2580, 2592, 2868, 4096, 8192, 13376, 16384, 32768, 32769, 32770, 32771, 32776, 32777, 32778, 32779, 32896, 32897 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 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. A set-system is uniform if all edges have the same size, and regular if all vertices appear the same number of times. LINKS FORMULA Intersection of A326783 and A326784. EXAMPLE The sequence of all uniform regular set-systems together with their BII-numbers begins:     0: {}     1: {{1}}     2: {{2}}     3: {{1},{2}}     4: {{1,2}}     8: {{3}}     9: {{1},{3}}    10: {{2},{3}}    11: {{1},{2},{3}}    16: {{1,3}}    32: {{2,3}}    52: {{1,2},{1,3},{2,3}}    64: {{1,2,3}}   128: {{4}}   129: {{1},{4}}   130: {{2},{4}}   131: {{1},{2},{4}}   136: {{3},{4}}   137: {{1},{3},{4}}   138: {{2},{3},{4}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Select[Range[0, 1000], SameQ@@Length/@bpe/@bpe[#]&&SameQ@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]&] CROSSREFS Cf. A000120, A029931, A048793, A070939, A319056, A319189, A321698, A326031, A326701, A326783 (uniform), A326784 (regular), A326788. Sequence in context: A069811 A004826 A326783 * A327080 A291621 A329268 Adjacent sequences:  A326782 A326783 A326784 * A326786 A326787 A326788 KEYWORD nonn AUTHOR Gus Wiseman, Jul 25 2019 STATUS approved

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Last modified April 17 22:19 EDT 2021. Contains 343071 sequences. (Running on oeis4.)