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 A326784 BII-numbers of regular set-systems. 10
 0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 16, 18, 25, 30, 32, 33, 42, 45, 51, 52, 63, 64, 75, 76, 82, 94, 97, 109, 115, 116, 127, 128, 129, 130, 131, 132, 136, 137, 138, 139, 140, 144, 146, 160, 161, 192, 256, 258, 264, 266, 288, 385, 390, 408, 427, 428, 434, 458 (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. A set-system is regular if all vertices appear the same number of times. LINKS Table of n, a(n) for n=1..59. EXAMPLE The sequence of all regular set-systems together with their BII-numbers begins: 0: {} 1: {{1}} 2: {{2}} 3: {{1},{2}} 4: {{1,2}} 7: {{1},{2},{1,2}} 8: {{3}} 9: {{1},{3}} 10: {{2},{3}} 11: {{1},{2},{3}} 12: {{1,2},{3}} 16: {{1,3}} 18: {{2},{1,3}} 25: {{1},{3},{1,3}} 30: {{2},{1,2},{3},{1,3}} 32: {{2,3}} 33: {{1},{2,3}} 42: {{2},{3},{2,3}} 45: {{1},{1,2},{3},{2,3}} 51: {{1},{2},{1,3},{2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Select[Range[0, 100], SameQ@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]&] CROSSREFS Cf. A000120, A001511, A005176, A029931, A048793, A070939, A295193, A322554, A326031, A326701, A326783 (uniform), A326785 (uniform regular). Sequence in context: A047549 A039074 A326966 * A047337 A039049 A037466 Adjacent sequences: A326781 A326782 A326783 * A326785 A326786 A326787 KEYWORD nonn AUTHOR Gus Wiseman, Jul 25 2019 STATUS approved

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Last modified September 16 12:57 EDT 2024. Contains 375976 sequences. (Running on oeis4.)