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A367913
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Least number k such that there are exactly n ways to choose a multiset consisting of a binary index of each binary index of k.
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10
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1, 4, 64, 20, 68, 320, 52, 84, 16448, 324, 832, 116, 1104, 308, 816, 340, 836, 848, 1108, 1136, 1360, 3152, 16708, 372, 5188, 5216, 852, 880, 2884, 1364, 13376, 1392, 3184, 3424, 17220, 5204, 5220, 2868, 5728, 884, 19536, 66896, 2900, 1396, 21572, 3188, 3412
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OFFSET
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1,2
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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:
1: {{1}}
4: {{1,2}}
64: {{1,2,3}}
20: {{1,2},{1,3}}
68: {{1,2},{1,2,3}}
320: {{1,2,3},{1,4}}
52: {{1,2},{1,3},{2,3}}
84: {{1,2},{1,3},{1,2,3}}
16448: {{1,2,3},{1,2,3,4}}
324: {{1,2},{1,2,3},{1,4}}
832: {{1,2,3},{1,4},{2,4}}
116: {{1,2},{1,3},{2,3},{1,2,3}}
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MATHEMATICA
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bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
spnm[y_]:=Max@@NestWhile[Most, y, Union[#]!=Range[0, Max@@#]&];
c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]], {n, 1000}];
Table[Position[c, n][[1, 1]], {n, spnm[c]}]
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CROSSREFS
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A version for multisets and divisors is A355734.
Positions of first appearances in A367912.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
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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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