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A368112
Sorted positions of first appearances in A368109 (number of ways to choose a binary index of each binary index).
9
1, 4, 20, 52, 64, 68, 84, 116, 308, 372, 820, 884, 1088, 1092, 1108, 1140, 1396, 1908, 2868, 2932, 3956, 5184, 5188, 5204, 5236, 5492, 6004, 8052, 13376, 13380, 13396, 13428, 13684, 14196, 16244, 17204, 17268, 18292, 19252, 19316, 20340, 22388, 24436, 30580
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}}
372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}
820: {{1,2},{1,3},{2,3},{1,4},{2,4}}
884: {{1,2},{1,3},{2,3},{1,2,3},{1,4},{2,4}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
c=Table[Length[Tuples[bpe/@bpe[n]]], {n, 1000}];
Select[Range[Length[c]], FreeQ[Take[c, #-1], c[[#]]]&]
CROSSREFS
For multisets we have A367915, unsorted A367913, firsts A367912.
Sorted positions of first appearances in A368109.
The unsorted version is A368111.
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: A160799 A187274 A367915 * A108099 A244050 A250224
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 17 2023
STATUS
approved