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A367915
Sorted positions of first appearances in A367912 (number of multisets that can be obtained by choosing a binary index of each binary index).
10
1, 4, 20, 52, 64, 68, 84, 116, 308, 320, 324, 340, 372, 816, 832, 836, 848, 852, 880, 884, 1104, 1108, 1136, 1360, 1364, 1392, 1396, 1904, 1908, 2868, 2884, 2900, 2932, 3152, 3184, 3188, 3412, 3424, 3440, 3444, 3952, 3956, 5188, 5204, 5216, 5220, 5236, 5476
OFFSET
1,2
COMMENTS
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}.
EXAMPLE
The terms together with the corresponding set-systems begin:
1: {{1}}
4: {{1,2}}
20: {{1,2},{1,3}}
52: {{1,2},{1,3},{2,3}}
64: {{1,2,3}}
68: {{1,2},{1,2,3}}
84: {{1,2},{1,3},{1,2,3}}
116: {{1,2},{1,3},{2,3},{1,2,3}}
308: {{1,2},{1,3},{2,3},{1,4}}
320: {{1,2,3},{1,4}}
324: {{1,2},{1,2,3},{1,4}}
340: {{1,2},{1,3},{1,2,3},{1,4}}
372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]], {n, 10000}];
Select[Range[Length[c]], FreeQ[Take[c, #-1], c[[#]]]&]
CROSSREFS
A version for multisets and divisors is A355734.
Sorted positions of first appearances in A367912, for sequences A368109.
The unsorted version is A367913.
A048793 lists binary indices, length A000120, sum A029931.
A058891 counts set-systems, covering A003465, connected A323818.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
Sequence in context: A294630 A160799 A187274 * A368112 A108099 A244050
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 16 2023
STATUS
approved