A367911 Sorted positions of first appearances in A367905.

1, 4, 7, 20, 68, 320, 352, 1088, 3136, 5184, 13376, 16704, 17472, 70720, 82240, 83008, 90112, 90176

Offset

1,2

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}.

Links

Table of n, a(n) for n=1..18.

Example

The terms together with the corresponding set-systems begin:
      1: {{1}}
      4: {{1,2}}
      7: {{1},{2},{1,2}}
     20: {{1,2},{1,3}}
     68: {{1,2},{1,2,3}}
    320: {{1,2,3},{1,4}}
    352: {{2,3},{1,2,3},{1,4}}
   1088: {{1,2,3},{1,2,4}}
   3136: {{1,2,3},{1,2,4},{3,4}}
   5184: {{1,2,3},{1,2,4},{1,3,4}}
  13376: {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
  16704: {{1,2,3},{1,4},{1,2,3,4}}
  17472: {{1,2,3},{1,2,4},{1,2,3,4}}
  70720: {{1,2,3},{1,2,4},{1,3,4},{1,5}}
  82240: {{1,2,3},{1,4},{1,2,3,4},{1,5}}

Mathematica

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

Crossrefs

Sorted positions of first appearances in A367905.

The unsorted version is A367910.

Multisets without distinctness are A367915, unsorted A367913.

Without distinctness we have A368112, unsorted A368111.

For sets instead of sequences we have A368185, unsorted 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, A309326, A326031, A326702, A326753, A367902, A367906, A367907, A367912, A368109, A368183.

Sequence in context: A111955 A244791 A220004 * A368185 A359603 A255512

Adjacent sequences: A367908 A367909 A367910 * A367912 A367913 A367914

Keyword

nonn,more

Author

Gus Wiseman, Dec 16 2023

Status

approved