A368184 - OEIS

%I #6 Dec 18 2023 08:28:33

%S 7,1,4,20,276,320,1088,65856,66112,66624,263232

%N 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 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 The terms together with the corresponding set-systems begin:

%e       7: {{1},{2},{1,2}}

%e       1: {{1}}

%e       4: {{1,2}}

%e      20: {{1,2},{1,3}}

%e     276: {{1,2},{1,3},{1,4}}

%e     320: {{1,2,3},{1,4}}

%e    1088: {{1,2,3},{1,2,4}}

%e   65856: {{1,2,3},{1,4},{1,5}}

%e   66112: {{1,2,3},{2,4},{1,5}}

%e   66624: {{1,2,3},{1,2,4},{1,5}}

%t nn=10000;

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t q=Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]],{n,nn}];

%t k=Max@@Select[Range[Max@@q], SubsetQ[q,Range[#]]&]

%t Table[Position[q,n][[1,1]],{n,0,k}]

%Y For strict sequences: A367910, firsts of A367905, sorted A367911.

%Y For multisets w/o distinctness: A367913, firsts of A367912, sorted A367915.

%Y For sequences w/o distinctness: A368111, firsts of A368109, sorted A368112.

%Y Positions of first appearances in A368183.

%Y The sorted version is A368185.

%Y A048793 lists binary indices, length A000120, sum A029931.

%Y A058891 counts set-systems, covering A003465, connected A323818.

%Y A070939 gives length of binary expansion.

%Y A096111 gives product of binary indices.

%Y Cf. A072639, A253317, A326031, A326702, A326753, A355739, A355741, A367771, A367906, A367907.

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Dec 18 2023