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A327041
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a(n) is the number whose binary indices are the union of the set-system with BII-number n.
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19
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0, 1, 2, 3, 3, 3, 3, 3, 4, 5, 6, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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22 is the BII-number of {{2},{1,2},{1,3}}, and 7 has binary indices {1,2,3}, so a(22) = 7.
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MATHEMATICA
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bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Total[2^Union@@bpe/@bpe[n]]/2, {n, 0, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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