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A368111
Least k such that there are exactly A003586(n) ways to choose a binary index of each binary index of k.
9
1, 4, 64, 20, 68, 52, 1088, 84, 308, 1092, 116, 5184, 820, 1108, 372, 5188, 2868, 1140, 13376, 884, 5204, 17204, 1396, 13380, 2932, 5236, 275520, 19252, 1908, 13396, 17268, 5492, 275524, 84788, 3956, 13428, 1324096, 19316, 6004, 275540, 215860, 18292, 13684
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}}
64: {{1,2,3}}
20: {{1,2},{1,3}}
68: {{1,2},{1,2,3}}
52: {{1,2},{1,3},{2,3}}
84: {{1,2},{1,3},{1,2,3}}
308: {{1,2},{1,3},{2,3},{1,4}}
116: {{1,2},{1,3},{2,3},{1,2,3}}
820: {{1,2},{1,3},{2,3},{1,4},{2,4}}
372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}
884: {{1,2},{1,3},{2,3},{1,2,3},{1,4},{2,4}}
MATHEMATICA
nn=10000;
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
dd=Select[Range[nn], Max@@First/@FactorInteger[#]<=3&];
qq=Table[Length[Tuples[bpe/@bpe[n]]], {n, nn}];
kk=Select[Range[Length[dd]], SubsetQ[qq, Take[dd, #]]&]
Table[Position[qq, dd[[n]]][[1, 1]], {n, kk}]
CROSSREFS
With distinctness we have A367910, sorted A367911, firsts of A367905.
For multisets we have A367913, sorted A367915, firsts of A367912.
Positions of first appearances in A368109.
The sorted version is A368112.
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: A362386 A361683 A111444 * A367913 A210935 A090561
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 17 2023
STATUS
approved