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).

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

Offset: 1

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:
      1: {{1}}
      4: {{1,2}}
      7: {{1},{2},{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 sequences we have A367911, unsorted A367910, firsts of A367905.

Multisets w/o distinctness: A367915, unsorted A367913, firsts of A367912.

Sequences w/o distinctness: A368112, unsorted A368111, firsts of A368109.

Sorted list of positions of first appearances in A368183.

The unsorted version is A368184.

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

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
c=Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]],{n,1000}];
Select[Range[Length[c]], FreeQ[Take[c,#-1],c[[#]]]&]