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A368184
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Least k such that there are exactly n ways to choose a set consisting of a different binary index of each binary index of k.
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7
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7, 1, 4, 20, 276, 320, 1088, 65856, 66112, 66624, 263232
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OFFSET
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0,1
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COMMENTS
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A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, 18 has reversed binary expansion (0,1,0,0,1) and binary indices {2,5}.
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LINKS
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EXAMPLE
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The terms together with the corresponding set-systems begin:
7: {{1},{2},{1,2}}
1: {{1}}
4: {{1,2}}
20: {{1,2},{1,3}}
276: {{1,2},{1,3},{1,4}}
320: {{1,2,3},{1,4}}
1088: {{1,2,3},{1,2,4}}
65856: {{1,2,3},{1,4},{1,5}}
66112: {{1,2,3},{2,4},{1,5}}
66624: {{1,2,3},{1,2,4},{1,5}}
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MATHEMATICA
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nn=10000;
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
q=Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]], {n, nn}];
k=Max@@Select[Range[Max@@q], SubsetQ[q, Range[#]]&]
Table[Position[q, n][[1, 1]], {n, 0, k}]
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CROSSREFS
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Positions of first appearances in A368183.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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