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 A326910 BII-numbers of pairwise intersecting set-systems. 14
 0, 1, 2, 4, 5, 6, 8, 16, 17, 20, 21, 24, 32, 34, 36, 38, 40, 48, 52, 56, 64, 65, 66, 68, 69, 70, 72, 80, 81, 84, 85, 88, 96, 98, 100, 102, 104, 112, 116, 120, 128, 256, 257, 260, 261, 272, 273, 276, 277, 320, 321, 324, 325, 336, 337, 340, 341, 384, 512, 514 (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. LINKS Table of n, a(n) for n=1..60. EXAMPLE The sequence of all pairwise intersecting set-systems together with their BII-numbers begins: 0: {} 1: {{1}} 2: {{2}} 4: {{1,2}} 5: {{1},{1,2}} 6: {{2},{1,2}} 8: {{3}} 16: {{1,3}} 17: {{1},{1,3}} 20: {{1,2},{1,3}} 21: {{1},{1,2},{1,3}} 24: {{3},{1,3}} 32: {{2,3}} 34: {{2},{2,3}} 36: {{1,2},{2,3}} 38: {{2},{1,2},{2,3}} 40: {{3},{2,3}} 48: {{1,3},{2,3}} 52: {{1,2},{1,3},{2,3}} 56: {{3},{1,3},{2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Select[Range[0, 100], stableQ[bpe/@bpe[#], Intersection[#1, #2]=={}&]&] CROSSREFS Intersecting set systems are A051185 (not-covering) or A305843 (covering). BII-numbers of set-systems with empty intersection are A326911. Cf. A006058, A048793, A326031, A326875, A326912, A326913. Sequence in context: A325680 A176654 A185867 * A326905 A327061 A326913 Adjacent sequences: A326907 A326908 A326909 * A326911 A326912 A326913 KEYWORD nonn AUTHOR Gus Wiseman, Aug 04 2019 STATUS approved

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Last modified September 23 11:05 EDT 2023. Contains 365544 sequences. (Running on oeis4.)