cp's OEIS Frontend

A368184 Least k such that there are exactly n ways to choose a set consisting of a different binary index of each binary index of k.

%I A368184 #6 Dec 18 2023 08:28:33
%S A368184 7,1,4,20,276,320,1088,65856,66112,66624,263232
%N A368184 Least k such that there are exactly n ways to choose a set consisting of a different binary index of each binary index of k.
%C A368184 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 A368184 The terms together with the corresponding set-systems begin:
%e A368184       7: {{1},{2},{1,2}}
%e A368184       1: {{1}}
%e A368184       4: {{1,2}}
%e A368184      20: {{1,2},{1,3}}
%e A368184     276: {{1,2},{1,3},{1,4}}
%e A368184     320: {{1,2,3},{1,4}}
%e A368184    1088: {{1,2,3},{1,2,4}}
%e A368184   65856: {{1,2,3},{1,4},{1,5}}
%e A368184   66112: {{1,2,3},{2,4},{1,5}}
%e A368184   66624: {{1,2,3},{1,2,4},{1,5}}
%t A368184 nn=10000;
%t A368184 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A368184 q=Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]],{n,nn}];
%t A368184 k=Max@@Select[Range[Max@@q], SubsetQ[q,Range[#]]&]
%t A368184 Table[Position[q,n][[1,1]],{n,0,k}]
%Y A368184 For strict sequences: A367910, firsts of A367905, sorted A367911.
%Y A368184 For multisets w/o distinctness: A367913, firsts of A367912, sorted A367915.
%Y A368184 For sequences w/o distinctness: A368111, firsts of A368109, sorted A368112.
%Y A368184 Positions of first appearances in A368183.
%Y A368184 The sorted version is A368185.
%Y A368184 A048793 lists binary indices, length A000120, sum A029931.
%Y A368184 A058891 counts set-systems, covering A003465, connected A323818.
%Y A368184 A070939 gives length of binary expansion.
%Y A368184 A096111 gives product of binary indices.
%Y A368184 Cf. A072639, A253317, A326031, A326702, A326753, A355739, A355741, A367771, A367906, A367907.
%K A368184 nonn,more
%O A368184 0,1
%A A368184 _Gus Wiseman_, Dec 18 2023