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.

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

Offset: 0

Author

Gus Wiseman, Dec 18 2023

Keywords

• nonn
• more

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}.

Examples

			The terms together with the corresponding set-systems begin:
      7: {{1},{2},{1,2}}
      1: {{1}}
      4: {{1,2}}
     20: {{1,2},{1,3}}
    276: {{1,2},{1,3},{1,4}}
    320: {{1,2,3},{1,4}}
   1088: {{1,2,3},{1,2,4}}
  65856: {{1,2,3},{1,4},{1,5}}
  66112: {{1,2,3},{2,4},{1,5}}
  66624: {{1,2,3},{1,2,4},{1,5}}
		

Crossrefs

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

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

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

Positions of first appearances in A368183.

The sorted version is A368185.

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.

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

Programs

Mathematica

nn=10000;
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
q=Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]],{n,nn}];
k=Max@@Select[Range[Max@@q], SubsetQ[q,Range[#]]&]
Table[Position[q,n][[1,1]],{n,0,k}]