cp's OEIS Frontend

A368185 Sorted list of positions of first appearances in A368183 (number of sets that can be obtained by choosing a different binary index of each binary index).

%I A368185 #6 Dec 18 2023 08:28:28
%S A368185 1,4,7,20,276,320,1088,65856,66112,66624
%N A368185 Sorted list of positions of first appearances in A368183 (number of sets that can be obtained by choosing a different binary index of each binary index).
%C A368185 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 A368185 The terms together with the corresponding set-systems begin:
%e A368185       1: {{1}}
%e A368185       4: {{1,2}}
%e A368185       7: {{1},{2},{1,2}}
%e A368185      20: {{1,2},{1,3}}
%e A368185     276: {{1,2},{1,3},{1,4}}
%e A368185     320: {{1,2,3},{1,4}}
%e A368185    1088: {{1,2,3},{1,2,4}}
%e A368185   65856: {{1,2,3},{1,4},{1,5}}
%e A368185   66112: {{1,2,3},{2,4},{1,5}}
%e A368185   66624: {{1,2,3},{1,2,4},{1,5}}
%t A368185 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A368185 c=Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]],{n,1000}];
%t A368185 Select[Range[Length[c]], FreeQ[Take[c,#-1],c[[#]]]&]
%Y A368185 For sequences we have A367911, unsorted A367910, firsts of A367905.
%Y A368185 Multisets w/o distinctness: A367915, unsorted A367913, firsts of A367912.
%Y A368185 Sequences w/o distinctness: A368112, unsorted A368111, firsts of A368109.
%Y A368185 Sorted list of positions of first appearances in A368183.
%Y A368185 The unsorted version is A368184.
%Y A368185 A048793 lists binary indices, length A000120, sum A029931.
%Y A368185 A058891 counts set-systems, covering A003465, connected A323818.
%Y A368185 A070939 gives length of binary expansion.
%Y A368185 A096111 gives product of binary indices.
%Y A368185 Cf. A072639, A253317, A326031, A326702, A326753, A355739, A355741, A367771, A367906, A367907.
%K A368185 nonn,more
%O A368185 1,2
%A A368185 _Gus Wiseman_, Dec 18 2023