A368183 Number of sets that can be obtained by choosing a different binary index of each binary index of n.

1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 3, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 1, 3, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 1, 3, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 3, 1, 1, 0, 1, 0, 0

Offset

0,5

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=0..86.

Example

The binary indices of binary indices of 52 are {{1,2},{1,3},{2,3}}, with choices (1,3,2), (2,1,3), both permutations of {1,2,3}, so a(52) = 1.

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Union[Sort/@Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]]], {n, 0, 100}]

Crossrefs

For sequences we have A367905, firsts A367910, sorted A367911.

Positions of zeros are A367907.

Without distinctness we have A367912, firsts A367913, sorted A367915.

Positions of positive terms are A367906.

For sequences without distinctness: A368109, firsts A368111, sorted A368112.

Positions of first appearances are A368184, sorted 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, A309326, A326031, A326702, A326753, A355739, A355741, A355744, A367771.

Sequence in context: A033665 A104234 A355905 * A367905 A321926 A037870

Adjacent sequences: A368180 A368181 A368182 * A368184 A368185 A368186

Keyword

nonn

Author

Gus Wiseman, Dec 17 2023

Status

approved