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 A330217 BII-numbers of achiral set-systems. 8
 0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 16, 25, 32, 42, 52, 63, 64, 75, 116, 127, 128, 129, 130, 131, 136, 137, 138, 139, 256, 385, 512, 642, 772, 903, 1024, 1155, 1796, 1927, 2048, 2184, 2320, 2457, 2592, 2730, 2868, 3007, 4096, 4233, 6416, 6553, 8192, 8330 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A set-system is a finite set of finite nonempty sets. It is achiral if it is not changed by any permutation of the vertices. 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 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 EXAMPLE The sequence of all achiral set-systems together with their BII-numbers begins:    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}}   16: {{1,3}}   25: {{1},{3},{1,3}}   32: {{2,3}}   42: {{2},{3},{2,3}}   52: {{1,2},{1,3},{2,3}}   63: {{1},{2},{3},{1,2},{1,3},{2,3}}   64: {{1,2,3}}   75: {{1},{2},{3},{1,2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]], i}, {i, Length[p]}])], {p, Permutations[Union@@m]}]]; Select[Range[0, 1000], Length[graprms[bpe/@bpe[#]]]==1&] CROSSREFS These are numbers n such that A330231(n) = 1. Achiral set-systems are counted by A083323. MG-numbers of planted achiral trees are A214577. Non-isomorphic achiral multiset partitions are A330223. Achiral integer partitions are counted by A330224. BII-numbers of fully chiral set-systems are A330226. MM-numbers of achiral multisets of multisets are A330232. Achiral factorizations are A330234. Cf. A000120, A003238, A016031, A048793, A070939, A326031, A326702, A327080, A327081, A330218, A330229, A330233. Sequence in context: A285405 A305441 A121405 * A231003 A171551 A096199 Adjacent sequences:  A330214 A330215 A330216 * A330218 A330219 A330220 KEYWORD nonn AUTHOR Gus Wiseman, Dec 06 2019 STATUS approved

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Last modified September 17 19:06 EDT 2021. Contains 347489 sequences. (Running on oeis4.)