cp's OEIS Frontend

A367911 Sorted positions of first appearances in A367905.

%I A367911 #6 Dec 17 2023 11:23:37
%S A367911 1,4,7,20,68,320,352,1088,3136,5184,13376,16704,17472,70720,82240,
%T A367911 83008,90112,90176
%N A367911 Sorted positions of first appearances in A367905.
%C A367911 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}.
%e A367911 The terms together with the corresponding set-systems begin:
%e A367911       1: {{1}}
%e A367911       4: {{1,2}}
%e A367911       7: {{1},{2},{1,2}}
%e A367911      20: {{1,2},{1,3}}
%e A367911      68: {{1,2},{1,2,3}}
%e A367911     320: {{1,2,3},{1,4}}
%e A367911     352: {{2,3},{1,2,3},{1,4}}
%e A367911    1088: {{1,2,3},{1,2,4}}
%e A367911    3136: {{1,2,3},{1,2,4},{3,4}}
%e A367911    5184: {{1,2,3},{1,2,4},{1,3,4}}
%e A367911   13376: {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
%e A367911   16704: {{1,2,3},{1,4},{1,2,3,4}}
%e A367911   17472: {{1,2,3},{1,2,4},{1,2,3,4}}
%e A367911   70720: {{1,2,3},{1,2,4},{1,3,4},{1,5}}
%e A367911   82240: {{1,2,3},{1,4},{1,2,3,4},{1,5}}
%t A367911 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A367911 c=Table[Length[Select[Tuples[bpe/@bpe[n]],UnsameQ@@#&]],{n,1000}];
%t A367911 Select[Range[Length[c]],FreeQ[Take[c,#-1],c[[#]]]&]
%Y A367911 Sorted positions of first appearances in A367905.
%Y A367911 The unsorted version is A367910.
%Y A367911 Multisets without distinctness are A367915, unsorted A367913.
%Y A367911 Without distinctness we have A368112, unsorted A368111.
%Y A367911 For sets instead of sequences we have A368185, unsorted A368184.
%Y A367911 A048793 lists binary indices, length A000120, sum A029931.
%Y A367911 A058891 counts set-systems, covering A003465, connected A323818.
%Y A367911 A070939 gives length of binary expansion.
%Y A367911 A096111 gives product of binary indices.
%Y A367911 Cf. A072639, A309326, A326031, A326702, A326753, A367902, A367906, A367907, A367912, A368109, A368183.
%K A367911 nonn,more
%O A367911 1,2
%A A367911 _Gus Wiseman_, Dec 16 2023